Question

A manufacturer of chandeliers is calculating the total cost of a new holiday themed light. The fixed cost f of producing the lights is $42,000. The unit cost u13 + 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

Answer 1

42,000 + 13q + 2.25q² (Model for total cost)

The total cost = $65,800

Explanation:

Given:

Total fixed cost = $42,000

Unit cost, u = 13 + 9v ..........(1)

where,

v is the vendor handling rate = 0.25q ..........(2)

where, q is the quantity produced = 100

substituting 2 in 1, we get

u = 13 + 9 × (0.25q)

or

u = 13 + 2.25q

Now,

for q number of quantities total unit cost = u × q

or

= (13 + 2.25q) × q

= 13q + 2.25q²

Therefore,

the total cost = Fixed cost + total unit cost

or

The total cost = 42,000 + 13q + 2.25q² (Model for total cost)

Hence, for q = 100

total cost = 42,000 + 13 × 100 + 2.25 × 100²

or

The total cost = 42000 + 1300 + 22500 = $65,800