# Thread: Maximum Profit and Minimum Cost(BIG ONE)

1. ## Maximum Profit and Minimum Cost(BIG ONE)

You are given the function p(q) at which q units of a particular commodity can be sold and the total cost c(q) of producing the q units: In each case

A)Find:
Revenue Function R(q), the profit function P(q), the marginal revenue R'(q), and the marginal cost C'(q). Sketch the graphs of p(q), R'(q), and C'(q) on the same coordinates axes and determine the level of production q where P(q) is maximized.

B)Find:
Average Cost A(q)=C(q)/q and sketch the graphs pf A(q), and the marginal cost C'(q) on the same axes. Determine Level of Production q at which A(q) is minimized.

I have the answers because its an odd question and the answers are in the back of the book..but I would like to know how they got the answers....If you can help sure appreciate it...have a bunch of these on my HW for next weak.

2. Originally Posted by lisa1984wilson
You are given the function p(q) at which q units of a particular commodity can be sold and the total cost c(q) of producing the q units: In each case

A)Find:
Revenue Function R(q), the profit function P(q), the marginal revenue R'(q), and the marginal cost C'(q). Sketch the graphs of p(q), R'(q), and C'(q) on the same coordinates axes and determine the level of production q where P(q) is maximized.

B)Find:
Average Cost A(q)=C(q)/q and sketch the graphs pf A(q), and the marginal cost C'(q) on the same axes. Determine Level of Production q at which A(q) is minimized.

I have the answers because its an odd question and the answers are in the back of the book..but I would like to know how they got the answers....If you can help sure appreciate it...have a bunch of these on my HW for next weak.
Alright economics time,

Revenue is Quantity of items sold* Price of items, so Revenue=P*Q which in this case is p(q)*q=(49-q)q=$\displaystyle 49q-q^2$

Marginal Revenue=R'(q)=49-2q

Profit is equal to Revenue-Cost, so it is $\displaystyle 49q-q^2-\frac{1}{8q^2}-4q-200=45q-q^2-\frac{1}{8q^2}-200$

Marginal cost=c'(q)=$\displaystyle 45-2q+\frac{1}{4q^3}$

Profit is maximized when marginal revenue=marginal cost so set the equations equal and find q

3. sorry I forgot to put the function on: its p(q)=49-q; C(q)=1/(8q^2)+4q+200

Can someone show me how to do this step by step because I missed classes because of the flu so I have not learned how to do these yet.

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