Question

The total cost in dollars to produce units of a product is C(q).Fixed costs are $19,500. The marginal cost is C' (q) = 0.00592 - +58 Round your answers to two decimal places. (a) Find C(200), the total cost to produce 200 units. The total cost to produce 200 units is (b) Find the value of C (200). C' (200) = $ (c) Use parts (a) and (b) to estimate C(201). C(201) =s

Answer 1

look at explanation

Step-by-step explanation: Given information:

Fixed cost (FC) = $19,500

Marginal cost (C') = 0.00592q + 58

(a) To find the total cost to produce 200 units, we need to evaluate C(200).

C(q) = integral of C'(q) with respect to q + FC

C(q) = (0.00592/2)q^2 + 58q + FC

C(200) = (0.00592/2)(200)^2 + 58(200) + 19,500

C(200) = $33,764

Therefore, the total cost to produce 200 units is $33,764.

(b) To find the value of C'(200), we can differentiate C(q) with respect to q:

C'(q) = 0.00592q + 58

So, C'(200) = 0.00592(200) + 58 = $59.84

Therefore, the value of C'(200) is $59.84.

(c) We can estimate C(201) using the marginal cost at q = 200:

C(201) ≈ C(200) + C'(200) * (201 - 200)

C(201) ≈ $33,764 + $59.84 * 1

C(201) ≈ $33,823.84

Therefore, the estimated cost to produce 201 units is $33,823.84.