Question

1. The manager of FrozonAir Refrigerator factory notices that on Monday it cost the company a total of $25,000 to build 30 refrigerators and on Tuesday it cost $30,000 to build 40 refrigerators. Find a linear cost function based on this information. What is the daily fixed cost, and what is the marginal cost?

Answer 1

Answer:

The fixed costs per day for the factory is $10,000 and marginal cost of one refrigerator for $500

Step-by-step explanation:

Let

Cost per refrigerator (marginal cost) = r

Fixed costs per day for the factory = f

Total cost = variable cost + fixed cost

Monday

25,000 = 30r + f

Tuesday

30,000 = 40r + f

Using Monday,

f = 25000 -30r

Substitute f = 25000 - 30r into Tuesday

30,000 = 40r + f

30,000 = 40r + (25,000 -30r)

30,000 = 40r + 25,000 - 30r

Collect like terms

30,000 - 25,000 = 40r - 30r

5,000 = 10r

Divide both sides by 10

r = 5,000 / 10

= 500

r = $500

Substitute r= 500 into Monday equation

f = 25,000 -30r

= 25,000 - 30(500)

= 25,000 - 15,000

= 10,000

f = $10,000

Therefore, the fixed costs per day for the factory is $10,000 and marginal cost of one refrigerator for $500