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.