The total cost in dollars to produce q units of a product is C (q). Fixed costs are $13000. The marginal cost is C' (q) = 0.006q^2-q+50.

Estimate C (170), the total cost to produce 170 units. Find the value of C' (170). Then combine these to find C (171).

Question

Mathematics

Katrina Aguilar

5 August, 11:11

The total cost in dollars to produce q units of a product is C (q). Fixed costs are $13000. The marginal cost is C' (q) = 0.006q^2-q+50.

Estimate C (170), the total cost to produce 170 units. Find the value of C' (170). Then combine these to find C (171).

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Answers (1)

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Karissa Huff · Answer 1

C (q) = ∫C' (q) dq = ∫ (0.006q^2 - q + 50) dq = 0.002q^3 - 1/2q^2 + 50q + c; where c = 13,000

C (170) = 0.002 (170) ^3 - 1/2 (170) ^2 + 50 (170) + 13000 = 9826 - 14450 + 8500 + 13000 = $16,876

C' (170) = 0.006 (170) ^2 - 170 + 50 = 173.4 - 120 = $53.40

Therefore, C (171) = C (170) + C' (170) = $16,876 + $53.40 = $16929.40

The total cost in dollars to produce q units of a product is C (q). Fixed costs are $13000. The marginal cost is C' (q) = 0.006q^2-q+50.Estimate C (170), the total cost to produce 170 units. Find the value of C' (170). Then combine these to find C (171).

The total cost in dollars to produce q units of a product is C (q). Fixed costs are $13000. The marginal cost is C' (q) = 0.006q^2-q+50.

Estimate C (170), the total cost to produce 170 units. Find the value of C' (170). Then combine these to find C (171).