Real-Life Applications of Optimization

Applications of Optimization

QUESTION #1

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?

Open Ended

Please key in your answer below. Demonstrate the steps taken to arrive at your final answer:

QUESTION #2

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:

Open Ended

What is the optimal retail price that the Gregory's should set in order to maximise their weekly profit?

QUESTION #3

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:

Open Ended

What should the price be set to maximise revenue gained from the season games?

QUESTION #4

Blockbuster is selling personal CD players. Answer the following:

Open Ended

The regular price for each CD player is $80. During a typical two weeks, the store sells 50 units. Past sales indicate that for every $2 decrease in price, Blockbuster sells 10 more units during two weeks. Calculate the price that will maximise the business' revenue.