Math 111 help compound arithmetic.

Question

The cost to manufacture a product is proportional to the quantity produced, with a cost of 75000 dollars per day when 500 items are produced. The cost to store n items is proportional to the square of n, with a daily storage cost of $1750 dollars when 500 items are stored. In addition, there is a fixed daily cost of $2000. The total daily cost, T when producing and storing n items is the sum of production, storage and fixed costs.

T=??

The answer is not

3.5n^2+1500n+2000

Answer 1

If Cost of production per day(C_p ) is proportional to number of items (n), then:

C_p = 75,000(n)/500

C_p = 150n

So, if Cost of storage is proportional to n²:

C_s = 1750n²/500²

C_s = 0.007(n²)

So total cost is the sum of these two equations and the fixed cost of 2000:

C(n) = 0.007n² + 150n + 2000

Now check the math by plugging in 500 for n and it should equal 75000 + 1750 + 2000:

0.007(500)² + 150(500) + 2000 = 75000 + 1750