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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?

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anthougo

Answer:

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

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

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