Question

Marketing tells you that if you set the price of an item at $10 then you will be unable to sell it, but that you can sell 500 items for each dollar below $10 that you set the price. Suppose your fixed costs total $3000, and your marginal cost is $2 per item. What is the most profit you can make?

Answer 1

The question is, how many can you sell at $10? Let's say it's 1000.

Then if there are x price reductions, you can sell 1000+500x

So, the revenue will be (1000+500x)(10-x)
The cost is 3000+2(1000+500x)

profit is revenue - cost. Use your real value instead of 1000, and the resultant function will just be a parabola. Find its vertex for maximum profit.

Answer 2

X=2000&P=1000