Question

The amount of profit, p, you earn by selling knives,k, can be determined by:p=200k-500. A) determine the constraints on profit and the constraints on the number of knives sold
B) what happens to your profit as you sell more knives.
C) is it possible to make $14,000 profit? explain.

Answer 1

The only restraints on profit result from the restriction on the domain which in turn place a restriction on profit.  

0≤k. Knives sold cannot be negative.

So the range of profit or p is:

p=[-500, +oo)

Profit increases as the number of knives sold increases.  $200 more profit is gained by each sale of a knife.

4000=200k-500

4500=200k

k=22.5

Since k is for knives sold, it must be an integer value, so a $4000 profit is not possible.  At 22, p=3900 and at 23, p=4100