Use your CVP formulas to solve the following. Port Williams Basketball Company makes Basketballs that sell for $39.99 each. Its fixed costs are $22,000 per month, and variable cost per unit is $13.50. a) What is the contribution Margin? b) What is the break-even point in units? c) What is the Contribution Rate? d) What is the Break-even Sales Revenue?

Answers

Answer 1

a) The contribution margin is the difference between the selling price and the variable cost per unit. In this case, the selling price is $39.99 and the variable cost per unit is $13.50.

Contribution Margin = Selling Price - Variable Cost per Unit
Contribution Margin = $39.99 - $13.50
Contribution Margin = $26.49

The contribution margin represents the amount of each unit's revenue that contributes towards covering the fixed costs and generating profit. In this case, for every basketball sold, $26.49 contributes towards covering the fixed costs and generating profit.

The contribution margin for Port Williams Basketball Company is $26.49 per unit.

b) The break-even point in units is the quantity at which the company's total revenue equals its total costs, resulting in neither profit nor loss. To calculate the break-even point, we need to consider the fixed costs and the contribution margin per unit.

Break-even Point in Units = Fixed Costs / Contribution Margin per Unit
Break-even Point in Units = $22,000 / $26.49
Break-even Point in Units ≈ 831.19

The break-even point in units for Port Williams Basketball Company is approximately 831.19 units. This means that the company needs to sell at least 832 units to cover its fixed costs and avoid a loss.

The break-even point for Port Williams Basketball Company is approximately 832 units.

c) The contribution rate, also known as the contribution margin ratio, is the contribution margin expressed as a percentage of the selling price. It represents the portion of each dollar of revenue that contributes to covering fixed costs and generating profit.

Contribution Rate = (Contribution Margin / Selling Price) * 100
Contribution Rate = ($26.49 / $39.99) * 100
Contribution Rate ≈ 66.24%

The contribution rate for Port Williams Basketball Company is approximately 66.24%. This means that for every dollar of revenue generated, 66.24 cents contribute towards covering the fixed costs and generating profit.

The contribution rate for Port Williams Basketball Company is approximately 66.24%.

d) The break-even sales revenue is the level of revenue at which the company's total costs are covered, resulting in neither profit nor loss. To calculate the break-even sales revenue, we need to multiply the break-even point in units by the selling price.

Break-even Sales Revenue = Break-even Point in Units * Selling Price
Break-even Sales Revenue = 832 * $39.99
Break-even Sales Revenue ≈ $33,247.68

The break-even sales revenue for Port Williams Basketball Company is approximately $33,247.68. This means that the company needs to generate at least $33,247.68 in sales to cover its fixed costs and avoid a loss.

The break-even sales revenue for Port Williams Basketball Company is approximately $33,247.68

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Related Questions

what are the answers to a, b, c, d?

Answers

Answer:

Step-by-step explanation:

A function, f(x),represents the height of a plant x months after being planted. Students measure and record the height on a
Select the appropriate domain for this situation.
OA.
the set of all real numbers
OB.
the set of all integers
O c.
the set of all positive integers
OD
the set of all positive real numbers

Answers

Answer:

I think the answer would be A or B, the best would be B.

Step-by-step explanation:

K so since it is monthly, it would not be all positive data. So you are left with A or B. Integers are numbers that are positive and negative so since the data can be a range of positive and negative numbers, that is why the data set of all integers (b) is the best choice.

Your welcome :D

Find the area of the figure shown.

Answers

Answer:220

Step-by-step explanation:

LET X BE THE LENGTH OF RECTANGLE AND FOR UPPER PORTION OF DIA GRAM BASE OF RIGHT ANGLE TRIANGLE SO X=20

LET Y BE WIDTH OF RECTANGLE SO Y=8

LET P BE THE PERPENDICULAR OF THE RIGHT TRIANGLE SO P=6

THEN

AREA OF RECTANGLE=LENGTH*WIDTH

SO AREA OF RECTANGLE BECOMES=(20)(8)=160

AND AREA OF RIGHT ANGLE TRIANGLE BECOMES=1/2(BASE*(PERPENDICULAR)

SO =1/2(20)(6)=60

SO THE TOTAL AREA OF THE DIAGRAM=AREA OF RIGHT ANGLE TRIANGLE+AREA OF RECTANGLE=160+60=220

Let p be a prime. Let K = F_p(t), let w = t^p - t and let F = F_p (w).
(a) Find a polynomial of degree p in F[x] for which t is a root. Use this to deduce an upper bound on [K: F].
(b) Show that the automorphism δ of K defined by δ (t) = t + 1 fixes F. Use this to factor the polynomial you wrote down in (a) into linear factors in K[x]
(c) Show that K is a Galois extension of F and determine the Galois group Gal(K/F).

Answers

The degree of the extension [K: F] ≤ p.

Suppose K = F_p(t) has transcendence degree n over F_p.

Then K is an algebraic extension of F_p(t^p).

(a) We need to find a polynomial of degree p in F[x] for which t is a root.

In F_p, we have t^p - t ≡ 0 (mod p).

So, we can write t^p ≡ t (mod p).

Since F_p[t] is a polynomial ring over F_p, we have t^p - t ∈ F_p[t] is an irreducible polynomial.

Hence the degree of the extension [K: F] ≤ p.

Suppose K = F_p(t) has transcendence degree n over F_p.

Then K is an algebraic extension of F_p(t^p).

The minimal polynomial of t over F_p(t^p) is x^p - t^p. Thus, [K: F_p(t^p)] ≤ p.

Since K/F_p is an algebraic extension, we have [K: F_p] = [K: F_p(t^p)][F_p(t^p): F_p].

Thus, [K: F_p] ≤ p².

Therefore, [K: F] ≤ p².

(b) We need to show that the automorphism δ of K defined by δ (t) = t + 1 fixes F.

Let f(x) be the polynomial obtained in part (a). Since f(t) = 0, we have f(t + 1) = 0. This implies δ (t) = t + 1 is a root of f(x) also.

Hence, f(x) is divisible by x - (t + 1). We can writef(x) = (x - (t + 1))g(x)for some g(x) ∈ K[x].

Since [K: F] ≤ p², we have deg(g) ≤ p.

Substituting x = t into the above equation yields 0 = f(t) = (t - (t + 1))g(t) = -g(t).

Therefore, f(x) = (x - (t + 1))g(x) = (x - t - 1)(a_{p-1}x^{p-1} + a_{p-2}x^{p-2} + ··· + a_1 x + a_0)where a_{p-1}, a_{p-2}, ..., a_1, a_0 ∈ F_p are uniquely determined.

(c) To show that K is a Galois extension of F and determine the Galois group Gal(K/F), we need to check that K is a splitting field over F.

That is, we need to show that every element of F_p(t^p) has a root in K.Since K = F_p(t)(t^p - t) = F_p(t)(w), it suffices to show that w has a root in K.

Note that w = t^p - t = t(t^{p-1} - 1).

Since t is a root of f(x) = x^p - x ∈ F_p[t], we have t^p - t = 0 in K. Thus, w = 0 in K.

Therefore, K is a splitting field over F_p(t^p).Since [K : F_p(t^p)] ≤ p, the extension K/F_p(t^p) is separable.

Therefore, the extension K/F_p is also separable. Hence, K/F_p is a Galois extension. The degree of the extension is [K: F_p] = p².

The Galois group is isomorphic to a subgroup of S_p. Since F_p is a finite field of p elements, it contains a subfield isomorphic to Z_p. This subfield is fixed by any automorphism of K that fixes F_p.

Since F_p(t^p) is generated by F_p and t^p, any automorphism of K that fixes F_p(t^p) is uniquely determined by its effect on t.

Since there are p choices for δ(t), the Galois group has order p. It follows that the Galois group is isomorphic to Z_p.

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SOMEONE PLS HELP SHEHSJHSHS

Answers

Answer:

1. Quadrant II

2. Quadrant IV

3. Y-axis

Step-by-step explanation:

Find the volume of each composite figure.

Answers

Answer:

630 in^3

Step-by-step explanation:

6 x 6 x 14 = 504

(0.5 x 3 x 6) x 14 = 126

504 + 126 = 630

Consider the functions F(x)= x^2+9x and g(x)=1/x.

F(g(-1))is ? , and G(f(1/2))is ? .

Answers

Answer:

a). -8 b). 4/19

Step-by-step explanation:

F(x)= x²+9x g(x)=1/x.

g(-1) = 1/ - 1

= -1

f(-1) = x²+9x

= -1² + 9(-1)

= 1 - 9

= -8

G(f(1/2))

f(1/2) = x²+9x

= 1/2² + 9(1/2)

= 1/4 + 9/2

= 19/4

g (19/4) = 1/x

= 1/19/4

= 4/19

Answer:

1). -8 2). 4/19

Step-by-step explanation:

F(x)= x²+9x g(x)=1/x.

g(-1) = 1/ - 1

= -1

f(-1) = x²+9x

= -1² + 9(-1)

= 1 - 9

= -8

G(f(1/2))

f(1/2) = x²+9x

= 1/2² + 9(1/2)

= 1/4 + 9/2

= 19/4

g (19/4) = 1/x

= 1/19/4

= 4/19

Determine the area and circumference of a circle with radius 12 cm.

Answers

The area of the circle is 452.16 cm², and the circumference is 75.36 cm.

To determine the area and circumference of a circle with a radius of 12 cm, we can use the formulas:

Area = π * r²

Circumference = 2 * π * r

The radius (r) is 12 cm, we can substitute this value into the formulas to find the area and circumference.

Area = π * (12 cm)²

= π * 144 cm²

≈ 3.14 * 144 cm²

≈ 452.16 cm²

The area of the circle is approximately 452.16 square centimeters.

Circumference = 2 * π * 12 cm

= 2 * 3.14 * 12 cm

≈ 75.36 cm

The circumference of the circle is approximately 75.36 centimeters.

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The graph of a system of equations is
shown below.

a. (2,0) and (0,3)
b. (-40,-50)
c. the system has no solution
d. the system has infinitely many solutions

Answers

Answer:

The system has no solution.

Step-by-step explanation:

In order for the system to have a solution, both graphs must have an intercept to each others. We see in the picture that both graphs are parallel and do not have any interceptions which we don't know the solution to the system.

That means if graphs are parallel and have no interceptions, there are no solutions. The system of equations are for finding the interceptions of both graphs. But of course! Parallel lines do not intercept.

If you have any questions, feel free to ask.

find the change-of-coordinates matrix from the basisB = {1-7t^2, -6 + t+43t^2, 1+6t} to the standard basis. Then write t^2 as a linear combination of the polynomials in B.

Answers

To find the change-of-coordinates matrix from basis B to the standard basis, we need to express the standard basis vectors as linear combinations of the vectors in B. Then, to write t^2 as a linear combination of the polynomials in B, we can use the change-of-coordinates matrix to transform t^2 into the coordinates with respect to B.

To find the change-of-coordinates matrix from basis B to the standard basis, we express the standard basis vectors as linear combinations of the vectors in B. Let's denote the standard basis vectors as e1, e2, and e3. We can write:

e1 = 1(1 - 7t^2) + 0(-6 + t + 43t^2) + 0(1 + 6t)

e2 = 0(1 - 7t^2) + 1(-6 + t + 43t^2) + 0(1 + 6t)

e3 = 0(1 - 7t^2) + 0(-6 + t + 43t^2) + 1(1 + 6t)

The coefficients in these equations give us the entries of the change-of-coordinates matrix.

To write t^2 as a linear combination of the polynomials in B, we can use the change-of-coordinates matrix. Let [t^2]_B represent the coordinates of t^2 with respect to B. Then, [t^2]_B = C[t^2]_std, where C is the change-of-coordinates matrix. We can solve this equation to find [t^2]_B.

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Randomly select a painted rock from a bag containing 4 purple rocks, 3 green rocks, 3 orange rocks, and 2 blue rocks.

Answers

Answer:

i got a orange

Step-by-step explanation:

I would choose blue rocks bestie

Simplify the following expressions to have fewer terms (MIDDLE SCHOOL)

5x-3+(4x-6)+2

4y+3-(8x-2)

Answers

Answer:

Install math calculator

Thank you

Answer:

x=1\9

Step-by-step explanation:

first part:

5x-3+4x+2

5x+4x-3+2

9x-1

9x=1

x=1\9 answer.

Which graph shows exponential decay?

Answers

Answer:

the first one

Step-by-step explanation:

the first one

wayfktgfydfug9ugi0b7ffiobv57f9pogasdfyuiohfdfhjkl

Answers

Answer:

Area of the circle = 572.3 square ft.

Step-by-step explanation:

Area of a circle is given by the formula,

Area of a circle = πr²

Here 'r' = Radius of the circle

Diameter of circle given in the picture = 27 ft

Radius of the circle = [tex]\frac{27}{2}[/tex]

= 13.5 ft

Area of the circle = π(13.5)²

The J.R. Simplot Company produces frozen French fries that are then sold to customers such as McDonald's. The "prime" line of fries has an average length of 6.00 inches with a standard deviation of 0.50 inch. To make sure that Simplot continues to meet the quality standard for "prime" fries, they plan to select a random sample of n = 100 fries each day. The quality analysts will compute the mean length for the sample. They want to establish limits on either side of the 6.00 inch mean so that the chance of the sample mean falling within the limits is 0.99. What should these limits be?

Answers

Answer:

(5.871 `; 6.127)

Step-by-step explanation:

Given :

Mean = 6

Standard deviation. σ = 0.5

Samplr size, n = 100

Zcritical at 99% confidence = 2.58

The confidence interval :

Mean ± margin of error

Margin of Error = Zcritical * σ / sqrt(n)

Margin of Error = 2.58 * 0.5/sqrt(100) = 0.129

Confidence interval :

Lower boundary = 6.00 - 0.129 = 5.871

Upper boundary = 6.00 + 0.129 = 6.129

(5.871 `; 6.127)

9. What measure of central tendency is usually the preferred number by researchers for describing a group of scores?

10. Using the following data, calculate the standard deviation: 115, 125, 145, 150, 115, 125

Answers

The measure of central tendency that is usually the preferred number by researchers for describing a group of scores is the mean.

2x = 3

Then x = 3/2

Factor completely x3 − 2x2 − 8x + 16.
(x + 2)(x2 + 8)
(x − 2)(x2 + 8)
(x + 2)(x2 − 8)
(x − 2)(x2 − 8)

Answers

The expression x^3 - 2x^2 - 8x + 16 can be factored as (x - 2)(x^2 - 8).

To factor the given expression x^3 - 2x^2 - 8x + 16, we can look for common factors or factor it using grouping. In this case, we can observe that the expression can be factored by grouping.

First, we can factor out a common factor of (x - 2) from the first two terms:

x^3 - 2x^2 - 8x + 16 = (x - 2)(x^2 - 8x - 8)

Now, we can further factor the quadratic expression (x^2 - 8x - 8) by factoring out a common factor of 8:

(x^2 - 8x - 8) = (x - 2)(x - 8)

Therefore, the complete factorization of the expression x^3 - 2x^2 - 8x + 16 is:

(x - 2)(x - 2)(x - 8) which can also be written as (x - 2)(x^2 - 8).

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gh¯¯¯¯¯¯ has endpoints g(−3, 2) and h(3, −2). find the coordinates of the midpoint of gh¯¯¯¯¯¯ . a. (−3, 0) b. (0, 2) c. (0, 0) d. (0, −2)

Answers

The coordinates of the midpoint of the line segment GH with endpoints G(-3, 2) and H(3, -2) are (0, 0). The correct option is (C).

To determine the coordinates of the midpoint of the line segment GH with endpoints G(-3, 2) and H(3, -2), we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint (M) are given by the average of the x-coordinates and the average of the y-coordinates of the endpoints.

Midpoint (M) = ((x1 + x2) / 2, (y1 + y2) / 2)

For GH, plugging in the coordinates, we have:

Midpoint (M) = ((-3 + 3) / 2, (2 + -2) / 2)

Midpoint (M) = (0, 0)

Therefore, the coordinates of the midpoint of GH are (0, 0), which corresponds to option c. (0, 0).

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