Question

A game company can produce 400 jigsaw puzzles at a total cost of $6,800 and 5,000 puzzles at a total cost of $16,000. The company sells these jigsaw puzzles for $5 each.

a. Determine the cost function assuming that it is linear

b. Determine the company’s revenue function

c. Determine the company’s profit function

d. Determine the number of jigsaw puzzles the company must produce and sell to break even

This is a practice problem and I'm not sure where to start

Could you show step by step so i may practice my other problems that are similar to this? Thanks.

Answer 1

The production cost consists of a fixed cost and a variable cost. The fixed cost remains same irrespective of the number of items produced, whereas the variable cost is proportional to the number of items produced. Let the fixed cost be K and variable cost per item be Y

K + 400Y = 6800----------------(1)

K + 5000Y = 16000-------------(2)

(2) - (1) => K - K + (5000-400)Y = 16000-6800

4600Y = 9200

Y = $2

Substitute the vlue of Y in (1)

K + 400x2 = 6800

K = $6000

a) Cost function is, Cost, C = 6000+2N, where N is the number of jigsaw puzzles produced

b) Revenue per item = $5

Revenue function = 5N

c) Profit function = Revenue - cost

= 5N - (6000 + 2N)

= 3N - 6000

d) For break even, the profit is 0

So, 3N - 6000 = 0

N = 2000

The company must produce and sell 2000 items to break even