Maximum profit questions

• May 10th 2009, 06:20 PM
Calliegirl319
Maximum profit questions
I have no idea where to start with this. I really could use some help. It would be great thanks. =)

The total cost C(q) of producing q goods is given by:

C(q)= .01q^3-.6q^2+13q

A) What is the maximum profit if each item is sold of \$7 (assume you sell everything you produce.)

B) Suppose exactly 34 goods are produced. They all sell when the price is \$7 each but for each \$1 increase in price 2 fewer goods are sold. Should the price be raised, and if so by how much?
• May 10th 2009, 08:16 PM
Jhevon
Quote:

Originally Posted by Calliegirl319
I have no idea where to start with this. I really could use some help. It would be great thanks. =)

The total cost C(q) of producing q goods is given by:

C(q)= .01q^3-.6q^2+13q

A) What is the maximum profit if each item is sold of \$7 (assume you sell everything you produce.)

profit = revenue - cost

the revenue for selling q items at \$7 each is 7q dollars.

Quote:

B) Suppose exactly 34 goods are produced. They a;; se;; wjem tje [roce os \$7 each but for each \$1 increase in price 2 fewer goods are sold. Should the price be raised, and if so by how much?
there seems to be some typo here you must fix
• May 11th 2009, 11:30 AM
Calliegirl319
hey I fixed it thanks.
• May 12th 2009, 07:38 PM
Jhevon
Quote:

Originally Posted by Calliegirl319
hey I fixed it thanks.

ok

Quote:

Originally Posted by Calliegirl319
B) Suppose exactly 34 goods are produced. They all sell when the price is \$7 each but for each \$1 increase in price 2 fewer goods are sold. Should the price be raised, and if so by how much?

ok, we will find the function that gives the profit.

let the revenue function be R(q), and the profit be P(q) ... this is for selling q items. then for selling 34 items, the profit is

P(34) = R(34) - C(34)

you can find C(34), since you were given C(q), just plug in 34 for q. now we have to find R(34).

first, we find R(q)

Revenue = price*(number of items sold)

we are told, when the price increases by 1, the number of items sold decreases by 2. that is, if the price goes up by \$q dollors, then the number of items sold decrease by 2q.

so, we can write price = 7 + q, and q can be zero or bigger (it is 0 if we don't raise the price, and bigger if we do).

and we can hence write number of items sold = 34 - 2q.

thus, R(q) = (7 + q)(34 - 2q)

and so finally, P(34) = R(34) - C(34), where R(q) is the function above.

to find out if we want to raise the price, you must find the maximum value for P(q) = R(q) - C(q). then you can see what the price must be to get the most profit.
• May 14th 2009, 05:44 PM
Calliegirl319
Thank you very much. I understand that now =)