Question

4) Tye-Dye Sports manufactures custom long boards and has fixed costs of $945.00 per week and total costs of $8070.00 if the weekly output is 15 boards.a) Write the equation for the cost function, C(x). x is the number of long boards.b) If the boards sell for $546.00 a piece, write the equation for the revenue function, R(x).c) Write the profit function, P(x).d) How many long boards will the company need to manufacture and sell each week to break even?

Answer 1

Tye-Dye Sports

a) Cost function, C(x) = $475x + $945 = $8,070

b) Revenue function, R(x) = $546x

c) Profit function, P(x) = R(x) - C(x)

d) To break-even, Fixed cost/Contribution per unit

= 13.3 or 14

Step-by-step explanation:

a) Data and Calculations:

Fixed costs = $945 per week

Total costs = $8,070 per week

Production units = 15 boards per week

Variable costs = Total costs minus fixed costs

= $7,125 ($8,070 - 945)

Variable cost per unit = $7,125/15 = $475

Cost function, C(x) = $475x + $945 = $8,070

Revenue function, R(x) = $546x

Profit function, P(x) = R(x) - C(x)

= $546x - ($475x + $945)

Contribution per unit = $546 - $475 = $71

To break-even, Fixed cost/Contribution per unit

= $945/$71 = 13.3 or 14