Mary is planning to do two part-time jobs, one in the retail store ABC and the other in the restaurant LMNO, to earn tuition. She decides to earn at least $120 per week. In ABC, she can work 5 to 12 hours a week, and in LMNO, she can work 4 to 10 hours a week. The hourly wages of ABC and LMNO are $6 per hour and $8 per hour, respectively. When deciding how long to work in each place, Mary hopes to

Question 1

This question is about the application of linear programming (LP). Part (b) is a continuation of Part (a), and Part (c) is not related to Parts (a) and (b).

(a)Mary is planning to do two part-time jobs, one in the retail store ABC and the other in the restaurant LMNO, to earn tuition. She decides to earn at least $120 per week. In ABC, she can work 5 to 12 hours a week, and in LMNO, she can work 4 to 10 hours a week. The hourly wages of ABC and LMNO are $6 per hour and $8 per hour, respectively. When deciding how long to work in each place, Mary hopes to make a decision based on work stress. According to reviews on the Internet, Mary estimates that the stress levels of ABC and LMNO are 1 and 2 for each hour of working, respectively (stress levels are between 1 and 5; a large value means a high work stress which may cause work and life imbalance). Since stress accumulates over time, she assumes that the total stress of working in any place is proportional to the number of hours she works in that place.

How many hours should Mary work in each place per week? State verbally the objective, constraints and decision variables. Then formulate the problem as an LP model. After that, solve it using the graphical solution procedure. Please limit the answer to within two pages.
(40 marks)

(b)The estimated stress level for working at ABC was obtained from a few, not many, reviews on the Internet, so the estimate is rough. If the true stress level is believed to be in the range of 1 to 1.5 and its exact value cannot be known, explain whether Mary is able to determine the best time allocation. Please limit the answer to within one page.

(10 marks)

(c)Suppose your friend Bob creates a YouTube video that explains how to formulate a problem as an LP and how to solve it. Bob invites you to make an introduction video to attract YouTube users from all walks of life to watch the full video. Write down your complete transcript, no more than 400 words.
(50 marks)