Question

ve 32. Sally is opening a small clothing boutique. The fixed costs are $5000 per month and variable costs are $20 per unit. Sally plans to sell each unit for $50. Her revenue equation is represented by R(x) = 2x ^ 2 + 4x + 200 Use this information and answer the following questions. A. Find the expense equation. B. Find the breakeven point(s) C. Calculate her expected profit. D. Find the maximum revenue she expects. E. Based on this information will she make the most money if she sells the items for $50 each? Why or why not.

Answer 1

A) The expense equation is y = 5,000 + 20x.

B) The break-even points are 167 units and $8,333.

C) Sally's expected profit is
`2x^2 - 16x - 4800`.

D) We cannot find the maximum revenue since the value of x is not provided.

E) This question is irrelevant since the value of x is not indicated.

The fixed costs per month = $5,000

Variable cost per unit = $20

Selling price per unit = $50

Contribution margin per unit = $30 ($50 - $20)

Contribution margin ratio = 30/50 = 3/5 = 0.6

Revenue equation, R(x) = 2x^2 + 4x + 200

R(x) =
`2x^2 + 4x + 200`

A) Expense Equation:

Let the total cost = y

Let the number of units = x

y = 5,000 + 20x

B) Break-even Points:

In units:

Break-even point = Fixed costs/Contribution margin per unit

= 5,000/30

= 167 units

In Dollars:

Break-even point = Fixed costs/Contribution margin ratio

= 5,000/0.6

= $8,333

C) Expected Profit =
`2x^2 + 4x + 200` - 5,000 + 20x

=
`2x^2 - 16x - 4800`