# Need assistance with calculating profit maximisation and revenue maximisation

1. Aug 15, 2011

### iceman87

Im having trouble with this equation and not sure if my calculations are correct, i think i have worked out the profit maximisation correct but am unsure how to calculate the revenue maximisation

1. Desktop Publishing Software Inc. develops and markets software packages for business computers. Although sales have grown rapidly during recent years, the company’s management fears that a recent onslaught of new competitors may severely retard future growth opportunities. Therefore, it is believed that the time has come to “get big or get out”. The marketing and accounting departments have provided management with the following monthly revenue and cost information:
TR = 1000Q – Q2
TC = 50,000 + 100Q

a) Calculate monthly quantity, price and profit at the revenue maximising level.

b) Calculate monthly quantity, price and profit at the profit maximising level.

So i managed to simplify the equation down to

= 1100 - 2Q

then so to get profit maximisation i need to get this = 0

so 1100 - 2Q = 0

Q = 550 quantity

then i need to put this back in the original equation so:

(1000*550 - 550squared ) - (50000 - 100*550)

= 252,500
so this is profit

do i then to get price divide 252,500/550 and get 459 as price?

Last edited: Aug 15, 2011
2. Aug 15, 2011

### HallsofIvy

Staff Emeritus

I don't understand this. What equation did you simplify and how?
What you should do, to maximize revenue, is differentiate 10000Q- Q^2. But the derivative is NOT "1100 -2Q".

then so to get profit maximisation i need to get this = 0

so 1100 - 2Q = 0

Q = 550 quantity

then i need to put this back in the original equation so:

(1000*550 - 550squared ) - (50000 - 100*550)

= 252,500
so this is profit

do i then to get price divide 252,500/550 and get 459 as price?[/QUOTE]

3. Aug 15, 2011

### Ray Vickson

You have Rev = 1000*Q - Q^2 and Cost = 50000 + 100*Q, so Profit = Rev - Cost = 1000*Q+Q^2-50000-100*Q = 900*Q - Q^2 - 50000. You should always write out the full expressions (after simplifying) before you start to try optimizing them.

RGV

4. Aug 15, 2011

### iceman87

so now that I have the 900Q - Q^2 - 50000

in differential calc that simplifies to 900Q - 2Q and i know how to work out quantity that is when you have to make the equation equal to 0

so 900 - 2Q = 0
Q = 450

then to get profit maximisation you have to put 450 back in the original equation

(1000*450 - 450^20) - (50000 1 + 100^450)

But how do you work out revenue maximisation?

Last edited: Aug 15, 2011
5. Aug 15, 2011

### Ray Vickson

You say "I have the 900Q - Q^2 - 50000 .. in differential calc that simplifies to 900Q - 2Q...". No, it dos not. Its *derivative* is 900Q - 2Q. The 900Q - Q^2 - 50000 just remains unchanged and does not simplify to anything!

Rev max? Well, how did you maximize profit? What is stopping you from doing the same thing for revenue?

RGV

6. Aug 15, 2011

### Staff: Mentor

Probably a typo with the extra factor of Q - the derivative is 900 - 2Q

7. Aug 15, 2011

### iceman87

Thanks for your help guys sorry I'm real bad at calculus so the terminology I use may be completely wrong.

I think I have worked out revenue maximization is this correct

MR = MC
900 - 2Q = 100
2Q = 800
Q = 400

At Q = 400,

(1000*400 – 400^2) – (50000 + 100*400)

= \$150,000

P = TR/Q

P = 150,000/400

P= 375