A vendor at a carnival sells cotton candy and caramel apples for $2.00 each. The vendor is charged $60 to set up his booth. Furthermore, the vendor’s average cost for each product he produces is approximately $0.80. a. Write a linear cost function representing the cost C(x) (in $) to the vendor to produce x products. b. Write a linear revenue function representing the revenue R(x) (in $) for selling x products. c. Determine the number of products to be produced and sold for the vendor to break even. d. If 60 products are sold, will the vendor make money or lose money?

Answer with its Explanation:

Requirement A. The cost function is equal to variable cost for "x" units and fixed cost which remains fixed. Hence:

Cost Function = C(x) = $60  +  $0.8x

Requirement B. The revenue for any units "x" sold can be calculated by simply multiplying "x" with sales price per unit. Which means that:

Revenue Function = R(x) = $2 * x  = $2x

Requirement C. Now we have to find the breakeven quantity and this could be calculated using the following formula:

Breakeven Point = Fixed Cost / (Selling Price per Unit  - Variable Cost Per Unit)

By putting values we have:

Breakeven Point = $60 / ($2 - $0.8)    = 50 units

Requirement D. As the number of units are above breakeven point (No profit and loss position), hence making sales above 50 units will generate profit for the company.

The profit for the company would be:

Total Profit = Contribution per unit * Units above Breakeven point

Total Profit = ($2 - $0.8)  *  10 Units = $12

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