Consider yourself as an entrepreneur at the Mall selling 5000 donuts a day at 50¢ each. When you raised the price to 70¢ each, the sale dropped to 4000 donuts per day. Now, assume that there is a linear relationship between the price and number of donuts sold. Further assume that there is a fix cost (overhead) of $1000 per day and the cost of each donut is 25¢. What would be the price of the donut to maximize the profit?
[Hint: Profit=Revenue - sale price per donuts - overhead ($1000);
P(x)=R(x) -S(x)-1000, where x is the increased price per donut; P, R, and C are respectively, profit per day, revenue per day, and price per donut. Here P, R and S are all expressed as function of x. Now,
R = n*S, where n is the number of donuts sold per day;
Sale price per donut is
S=(0.5 + x) in dollar, where x is increased price per donut in dollar;
Number of donuts sold at price $(0.5+x) is, n=5000-(5000-4000/0.2)x=5000-5000*x=5000(1-x)