Question

MANUFACTURING

A manufacturer's total cost is C(q) = 0.1q ^ 3 - 0.5q ^ 2 + 500q + 200 dollars when q thousand units are produced . Currently , 4,000 units (q = 4) are being produced and the manufacturer is planning to increase the level of production to 4,100 . Use marginal analysis to estimate how this change will affect total cost .

Answer 1

Total cost is $205328

Explanation:

Given data:

cost C(q) = 0.1 q^3 - 0.5 q^2 + 500 q + 200

current units q = 4 ( 4000 units )

The current level of production is 4000 ( 4 )units, and manufacturer is planning to upgrade this to 4100 ( 4.1 ) units

C'(q) = 3 * 0.1 q^2 - 2 * 0.5 q + 500

C'(q) = 0.3 q2 - q + 500

C(4.1) - C(4) ≈ C’(4) x Δq

≈ C’(4) x 0.1

≈ ( 0.3 * 4^2 - 4 + 500 ) x 0.1

≈ ( 0.3 * 16 - 4 + 500 ) x 0.1

≈ 500.8 x 0.1 ≈ 50.08

total cost = 4100 x 50.08 = $205328