# Maximise profit

1. Apr 10, 2004

### sand7000

If the cost of one unit is $10, 20 units will be sold. If the cost is$11, 18 units will be sold. a) Find the demand function assuming it is linear.
b) If the materials for each unit cost \$6 what should the selling price be to maximise profit?

I believe that the demand function is p(x)=-.5x+20 but I cannot figure out how to maximise profit. PLEASE HELP!

2. Apr 10, 2004

### Chen

If d(p) is the demand as a function of the price, you know that:

d(p) = Ap + B

You need to find A and B. You have two pairs of values for d(p) and p, so use them to find A and B:

20 = 10A + B
18 = 11A + B

The function you posted does not seem correct.

The cost of all units would be 6*d(p). The return value would be d(p)*p. The profit is the difference:

f(p) = d(p)*p - 6*d(p)

Now replace d(p) with the actual function:

f(p) = (Ap + B)*p - 6*(Ap + B) = Ap2 + Bp - 6Ap - 6B

Find the derivative of f(p), see where it equals zero, etc etc.