Price optimization - three different products competing...

Hey there!

I've spent some time looking at this...

What I have is...

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Three products A, B and C (they are advertisements)...

The maximum advertisement-space in the newspaper is 150.000 mm.

If you rise the price of $5 on each of the products a decrease in sales will happen...

A: $5 increase on price 35 to 40
50.500 mm falls 6.000 mm to 44.500 mm

B: $5 increase on price 20 to 25
17.500 mm falls 4.000 mm to 13.500 mm

c: $5 increase on price 30 to 35
85.500 mm falls 15.000 mm to 70.500 mm

Okay, so what I need to find out is the optimal price-structure...


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Approaches I've tried so far...

I've tried to find the max revenue - by finding the function of the line for each of the products and - used integration to find the area underneath - and maximised the revenue (area underneath) - with the solver-function in Excel. I was not really a success, because they were all dependant on the same x.

Then I tried to solve it using help in the math-forum - (searching for price optimization), when I found an example by Fredrik, who made a function and derived it - f ' (x) = 0 is max - which makes perfectly sense, but - that doesn't take in to account the other functions...

Any help will be greatly appreciated... I think we supposed to solve it using the solver-function in Excel, but any help is appreciated... : o )