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:Total cost is $205328Step-by-step 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 ) unitsC'(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