Cost Function (Marginal Analysis Optimal Values)  TOPIC_SOLVED

Limits, differentiation, related rates, integration, trig integrals, etc.

Cost Function (Marginal Analysis Optimal Values)

Postby zedman1701 on Mon Dec 02, 2013 5:11 pm

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.
zedman1701
 
Posts: 1
Joined: Mon Dec 02, 2013 5:08 pm

Sponsor

Sponsor
 

Re: Cost Function (Marginal Analysis Optimal Values)  TOPIC_SOLVED

Postby buddy on Mon Dec 02, 2013 8:45 pm

zedman1701 wrote: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)?

zedman1701 wrote:ii. Find the marginal cost function and hence find the marginal cost when whe q=5

Do the derivative. Plug in q = 5.

zedman1701 wrote:iii. Interpret the marginal cost found in (ii).

Say in words what the marginal-cost function estimates.

zedman1701 wrote: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

zedman1701 wrote:ii. Find the marginal profit when x =60 interpret it.

Do the derivative. Say in words what the function means.

zedman1701 wrote: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.
buddy
 
Posts: 132
Joined: Sun Feb 22, 2009 10:05 pm


Return to Calculus