QUESTION 9 A manufacturer of chandeliers is calculating the total cost of a new

Question

QUESTION 9 A manufacturer of chandeliers is calculating the total cost of a new holiday themed light. The fixed cost fof producing the lights is $42,000. The unit cost u 13+9v, where v is the vendor handling rate per light. That rate is v = 0.25q , where q is the quantity produced. Develop a model for total cost. Then evaluate your model when 100 lights are produced. What is the total cost? Enter your answer as a whole number WITHOUT commas (example: enter 100 for $100.00 or enter 1000 for $1,000).

Explanation / Answer

Let the total number of lights produced be q.

Then the vendor handling rate per light, v = 0.25*q

The unit cost of one light, u = 13 + 9v = 13 + 9*0.25*q = 13 + 2.25*q

The fixed cost, f = 42000

Total Cost = f + q*u = 42000 + q(13 + 2.25q)

Total cost = 2.25q^2 + 13q + 42000

If q = 100,

Total Cost = 2.25(100)^2 + 13(100) + 42000 = 65800

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