Real-Life Applications of Optimization

A real estate office manages 50 condominium units in a downtown building. When the rent is $900 per month, all the units are occupied. For every $25 increase in rent, one unit becomes vacant. On average, all units require $75 in maintenance and repairs each month. How much rent should the real estate office charge to maximise profits?

Mr. and Ms. Gregory operates a bake shop. One of their specialties is the Nutella cheesecake. The cakes are bought from a supplier who charges $7.00 per cake, and they sell 200 cakes weekly at $11.00 each. Research shows that profit from the cake sales can be increased by increasing the price. Unfortunately, for every increase of $0.50 cents, sales will drop by 7 cakes. Answer the following:

The ongoing NBA season in Wellsring stadium has the capacity to hold 20,000 spectators. Average attendance at each game has been 14,000. The average ticket price is $75. Market research shows that for each $5 reduction in the ticket price, attendance increases by 800. Answer the following:

Blockbuster is selling personal CD players. Answer the following: