Aused car dealership has just opened in town. The facilities allow it to have up to 20 cars on the lot, including trade-ins and cars for sale. This dealership focuses on a very specific segment: very expensive classic cars.The owner knows that average prices fluctuate throughout the year as customers change preferences with the seasons. The expected average value per car is forecasted below.The owner looks for these rare classics all over the world. His plan is to spend some months buying cars around the world and other months selling them back home. Based on previous experience, he won't be able to buy more than 10 carsnor sell more than 15 during any given month. The dealer starts with an inventory of 20 cars (full lot), but his plan is to get out of this business at the end of the year (all cars must be sold by them). Using LP, find the expected maximum profit and optimal strategy.

a. What is the final profit

b.When should he buy cars

c.How many cars should he buy per month

d.When shouldhe sell cars

e.How many cars should he sell per month

Month (t) Car Prices

Jan 100,000

Feb 98,000

March 132,000

April 150,000

May 160,000

June 185,000

July 190,000

August 190,000

Sept 175,000

Oct 130,000

Nov 122,000

Dec 115,000