This question includes and (operation research) course.

Question #2. (3 Marks) Al-Haya Medical Company produces precision medical diagnostic equipment at two factories. Three pharmacies have placed orders for this month's production output. The table below shows what the cost would be for shipping each unit from each factory to each of these pharmacies. Also shown are the number of units that will be produced at each factory and the number of units ordered by each pharmacy. From Factory 1 Factory 2 Order size Unit Shipping Cost Pharmacy 1 Pharmacy 2 Pharmacy 3 $300 $400 $400 $200 $500 $300 150 units 200 units 200 units Factory Output 300 units 250 units A decision now needs to be made about the shipping plan for how many units to ship from each factory to each customer. a. [1 Mark] Formulate a linear programming model for this problem. b. [1 Mark] Solve the problem and discuss the optimal solution obtained upon solving (show the output of the software you used). c. [0.5 Mark] What is the optimal solution to the problem? d. [0.5 Mark] What is the optimal objective value? ANSWER Question #3. (5 Marks) A Jubail family owns 100 acres of farmland on which they plant rice and tomato. Each acre of rice costs SAR60 to plant, cultivate, and harvest; each acre of tomato costs SAR80. The family has a budget of SAR10,000 for next year. The family considered that the number of acres of tomato that can be planted to 20 acres. The profit from each acre of rice is SAR40; the profit from each acre of tomato is SAR60. The Jubail family wants to know how many acres of rice and tomato to plant in order to maximize their profit. a. Formulate a linear programming model for this problem. b. Solve the problem using computer (show the computer output). c. How many acres of farmland will not be cultivated at the optimal solution? d. Does the Jubail family use the entire 20-acre tomato allotment? e. If the family can obtain an additional 50 acres of land, will the number of acres of rice and tomato they plan to grow change? Explain. f. If the family decides not to cultivate a 30-acre section as part of a crop recovery program, will the number of acres of rice and tomato they plan to grow change? Explain. g. The Jubail family has an opportunity to lease some extra land from a neighbor. The neighbor is offering the land to them for SAR60 per acre. Should the family lease the land at that price? Explain. h. What is the maximum price the Jubail family should pay their neighbor for the land, and how much land should they lease at that price? i. The family is considering taking out a loan to increase their budget. For each dollar they borrow: i. how much additional profit would they make? ii. If they borrowed an additional SAR1,000, would the number of acres of rice and tomato they plant change