In: Math

Suppose a company has fixed costs of $47,600 and variable cost
per unit of 4/9*x* + 333 dollars,

where *x* is the total number of units produced. Suppose
further that the selling price of its product is

1767 −5/9x dollars per unit.

(a) Find the break-even points. (Enter your answers as a
comma-separated list.)

*x* =

(b) Find the maximum revenue. (Round your answer to the nearest
cent.)

$

(c) Form the profit function *P*(*x*) from the cost
and revenue functions.

*P*(*x*) =

Find maximum profit.

$

(d) What price will maximize the profit? (Round your answer to the
nearest cent.)

$

Fixed cost is 47,600;

Variable cost is 4x/9 + 333

Selling price per units = 1767-5x/9 per unit

For break even: Fixed cost + variable cost /unit * number of units
= selling price* number of units

Fixed cost = (selling price - variable cost) * number of
units

47600 = (1767 - 5x/9 - 4x/9 -333) * x

x ( 1434 - x) = 47600

x^{2} - 1434 x + 47600 =0;

x= 1400; x=34;

Break even points = 34 units and 1400 units;

b) Maximum revenue = (1767-5x/9) (x) = 1767x -
5x^{2}/9;

For maximum revenue, dR/dx =0 so

1767 - 10x/9 =0;

x= 1767*9/10 = 1590.3~= 1590; Since number of unit sold cant be a
decimal;

If x=1590, then total revenue = 1590 ( 1767-5(1590)/9) = 1590 (
883.66) =1,405,030$

c) Profit function = (SP - CP) *number of units

= (1767-5x/9)x - (47600 + x(4x/9 + 333)) = 1767x - 5x^{2}/9
- 47600 -4x^{2}/9 -333x

= -x^{2} + 1434x -47600

For maximum profit, dP/dx =0;

-2x + 1434=0

x= 1434/2= 717;

At x=717, P(x) = - 717^{2} + 1434(717) - 47600 =
4,66,489$

Thus, maximum profit occurs at 717 units which is = 466,489$

d) Price that maximises the profit is :

1767 - 5(717)/9 = 1767 - 398.33 = 1368.67$

Suppose a company has fixed costs of $48,000 and variable cost
per unit of
4
9
x + 333 dollars,
where x is the total number of units produced. Suppose
further that the selling price of its product is
2357 −
5
9
x dollars per unit.
(a) Find the break-even points. (Enter your answers as a
comma-separated list.)
x =
(b) Find the maximum revenue. (Round your answer to the nearest
cent.)
$
(c) Form the profit function P(x)...

1) Suppose that a company has fixed costs of $15 per unit and
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Steven Company has fixed costs of $239,080. The unit selling
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Product
Selling Price
per unit
Variable Cost
per unit
Contribution Margin
per unit
X
$1,248
$468
$780
Y
473
253
220
The sales mix for products X and Y is 60% and 40% respectively.
Determine the break-even point in units of X and Y combined. Round
answer to nearest whole number.
units...

Steven Company has fixed costs of $239,080. The unit selling
price, variable cost per unit, and contribution margin per unit for
the company's two products are provided below.
Product
Selling Price
per unit
Variable Cost
per unit
Contribution Margin
per unit
X
$1,248
$468
$780
Y
473
253
220
The sales mix for products X and Y is 60% and 40% respectively.
Determine the break-even point in units of X and Y combined. Round
answer to nearest whole number.
units

Suppose a company has fixed costs of $5,500 and variable costs
per unit of 7/8x + 1,040 dollars,
where x is the total number of units produced. Suppose
further that the selling price of its product is 1,200 − 1/8
x dollars per unit.
(a)
Form the cost function and revenue function (in dollars).
C(x)
=
R(x)
=
Find the break-even points.
x =
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(b)
Find the vertex of the revenue function.
(x, y) =
Identify the maximum revenue....

A company has $30 per unit in variable costs and $1,200,000 per
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Assume Phony Company has variable costs per unit of $23, fixed
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If the sales price per unit decreases by $4 and the variable cost
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A. Break-even point stays the same.
B. Break-even point increases.
C. Break-even point in dollars decreases.
D. Break-even point in dollars decreases and break-even point in
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Bob makes widgets. Variable costs per unit are $2. Fixed cost
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A wireless Bluetooth headphone manufacturer has a variable cost
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