# Calculus Maximize Problems...

• Mar 26th 2009, 02:45 PM
fifinambo
Calculus Maximize Problems...
I don't really get the steps to take for these two problems. Thank you guys for your help! :D

1.) C(q)=q3–75q2+1875q+1070 for 0q50 and a price per unit of \$500.

a) What production level maximizes profit?
q =

b) What is the total cost at this production level?
cost = \$

c) What is the total revenue at this production level?
revenue = \$

d) What is the total profit at this production level?
profit = \$

2.) Suppose the cost function for producing gadgets is C(q)=004q2+5q+44.

At what production level is the maximal profit achieved if each item is sold for 7 dollars? Answer: items.

What is the maximum profit if each item is sold for 7 dollars? Answer: dollars.
• Mar 26th 2009, 04:07 PM
fifinambo
I just realized there was some problems with my post. Sorry about that.
Anyway, I think the #1.)answer for a:38, and b:\$18,892. I don't know what to do for the rest though.(Wondering)

1.) C(q)=q^3–75q^2+1875q+1070 for 0<q<50 and a price per unit of \$500.
^--(These are "equal to" as well)

a) What production level maximizes profit?
q =

b) What is the total cost at this production level?
cost = \$

c) What is the total revenue at this production level?
revenue = \$

d) What is the total profit at this production level?
profit = \$

2.) Suppose the cost function for producing gadgets is C(q)=0.04q^2+5q+44.

At what production level is the maximal profit achieved if each item is sold for 7 dollars? Answer:

What is the maximum profit if each item is sold for 7 dollars? Answer:
• Mar 26th 2009, 07:07 PM
sinewave85
Quote:

Originally Posted by fifinambo
I just realized there was some problems with my post. Sorry about that.
Anyway, I think the #1.)answer for a:38, and b:\$18,892. I don't know what to do for the rest though.(Wondering)

1.) C(q)=q^3–75q^2+1875q+1070 for 0<q<50 and a price per unit of \$500.
^--(These are "equal to" as well)

a) What production level maximizes profit?
q =

b) What is the total cost at this production level?
cost = \$

c) What is the total revenue at this production level?
revenue = \$

d) What is the total profit at this production level?
profit = \$

2.) Suppose the cost function for producing gadgets is C(q)=0.04q^2+5q+44.

At what production level is the maximal profit achieved if each item is sold for 7 dollars? Answer:

What is the maximum profit if each item is sold for 7 dollars? Answer:

(Edit: This was my initial response, which I quickly modified to what follows. I am putting it back because the thread does not make sense without it) Is that a cost equation or a revenue equation?

Ok, well the calculus for this problem may be a bit advanced for me, but assuming that your answer for a) is correct, wouldn't the total revenue just be 38*500 = 19000? And that would make the total profit 19000 - 18,892 = 108.

Edit: Ok, thinking back to my economics and using my graphing calculator, I can at least confirm the answer for a), albeit in a rather informal way. Profit occurs when total cost is less than total revenue, and in this case that only happens on the interval specified between about x = 36.199418 and x = 39.54799. The distance between the curves appears to be greatest around x = 38, and testing seems to bear this out. Profit is \$71 at x = 37 and \$61 at x = 39. So whatever you did to find the value for q in Problem 1 should work for Problem 2. The total profit is just (number of units sold)*(price per unit) - (total cost).
• Mar 26th 2009, 07:21 PM
fifinambo
I believe it's a cost equation.
• Mar 26th 2009, 07:55 PM
sinewave85
Quote:

Originally Posted by fifinambo
I just realized there was some problems with my post. Sorry about that.
Anyway, I think the #1.)answer for a:38, and b:\$18,892. I don't know what to do for the rest though.(Wondering)

2.) Suppose the cost function for producing gadgets is C(q)=0.04q^2+5q+44.

At what production level is the maximal profit achieved if each item is sold for 7 dollars? Answer:

What is the maximum profit if each item is sold for 7 dollars? Answer:

On Problem 2, there appears to be no q on [0,50] for which a profit is possible, since C(q) is always greater than 7q on that interval.