SECTION B This section consists of FIVE (5) compulsory question. Candidates should attempt ALL parts of the question. Th

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Section B This Section Consists Of Five 5 Compulsory Question Candidates Should Attempt All Parts Of The Question Th 1 (89.84 KiB) Viewed 26 times

SECTION B This section consists of FIVE (5) compulsory question. Candidates should attempt ALL parts of the question. This section is worth SEVENTY-SIX (76) marks. B-1. As a side business, Mr Happy, keeps a fleet of luxury limousines that he rents out to a few individual clients. Each client needs at most 1 limo. The demand per week (i.e., the total number of customers per week) for Mr Happy's limos has the following probability distribution: Demand/Week O 1 2 3 4 3 Probability 0.05 0.2 0.5 0.2 0.05 (a) What is the expected value and the variance of the demand per week? [4 MARKS] (b) Suppose Mr. Happy has only 3 limos. It costs Mr. Happy £3,000 per week to maintain each limousine and his rental price per limo per week is £4,000. What is his expected weekly profit? [6 MARKS] (c) What is the probability that Mr. Happy makes a profit in a randomly chosen week? [3 MARKS] (d) Now suppose that you want to enter this business with the same demand distribution as Mr. Happy. You have to decide how many limos you want to own to maximize your expected profit. The cost of maintaining each limo and the rental price is the same as Mr. Happy. How many limos should you own? (5 MARKS]