## Cost Function (Marginal Analysis Optimal Values)

Limits, differentiation, related rates, integration, trig integrals, etc.
zedman1701
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### Cost Function (Marginal Analysis Optimal Values)

Marginal Analysis Optimal Values

1. The cost function for a product is given by C (q)= 100+60q + 3q²

i. Estimate the marginal cost when q= 5
ii. Find the marginal cost function and hence find the marginal cost when whe q=5
iii. Interpret the marginal cost found in (ii).

2. Freeze more Company has a cost function and a demand equation C (x)=2x²+15x+1500 and a demand equation p (x)=-0.3x+400

i. Determine the profit function.
ii. Find the marginal profit when x =60 interpret it.
iii. Determine the maximum profit.

3. New line products hires a consulting firm that determines its demand function to be p(x)=23 and its cost function to be C(x)=0.001x²+4x+5000

i. Find the profit function.
ii. Find the marginal profit function.
iii. Determine the value of that maximizes profit.
iv. Find the maximum profit.

4. The average cost function for a product is given by C(x) =0.7x - 21 21 + 1000/x

i. Find the cost function.
ii. Find the marginal cost function.
iii. Determine the value of x that maximize profit
iv. Find the minimum cost.

buddy
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### Re: Cost Function (Marginal Analysis Optimal Values)

1. The cost function for a product is given by C (q)= 100+60q + 3q²

i. Estimate the marginal cost when q= 5
They show here and here how to do marginal costs. But the estimate is supposed to be the marginal-cost fcn but you don't do that until the next part, so maybe your book means C(5)-C(4)?
ii. Find the marginal cost function and hence find the marginal cost when whe q=5
Do the derivative. Plug in q = 5.
iii. Interpret the marginal cost found in (ii).
Say in words what the marginal-cost function estimates.
2. Freeze more Company has a cost function and a demand equation C (x)=2x²+15x+1500 and a demand equation p (x)=-0.3x+400

i. Determine the profit function.
Do the def: profit = rev - cost
ii. Find the marginal profit when x =60 interpret it.
Do the derivative. Say in words what the function means.
iii. Determine the maximum profit.
Do the max/min thing. (Profit is a neg quadratic so the max/min pt is a max.)

Probs 3 & 4 work the same way. Please write back if you don't get the right answers. Thanks.