SCOM 361 Assignment 1 Fall 2017 This Assignment is worth 10%. It can be done by one, two, or three students (no more than three). Deadline: October 16, 23:55 Instructions: Please submit your assignment either as an MSWord or a pdf file on Moodle. The submission icon is placed in Week 16 Oct. - 22 Oct. To formulate and solve the problems, you may use the graphical method when this is possible (graph has to be included) or Lingo (output has to be included) To Do: P1, P2, P3 and P4 given below Chapter 3; Problem 29 Chapter 4; Case 1 Marking scheme P1 P2 Model 2 Model 4 Graph 2 Lingo 1 Sol. 1 Sol. 1 S=1 1 Total Total 5 7 P3 A B C D Total 6 3 3 3 15 P4 A 3 B 2 C 6 D 3 E 2 Total 16 Ch. 3; P. 29 Ch. 4; Case 1 a 2 1 6 b 5 2 3 c 2 3 3 d 2 4 3 e 2 5 5 f 2 Total Total 17 20 Grand total = 5+7+15+16+17+20 = 80 points = 10% of the course mark. Late assignments class policy: Late assignments, for any reason, will be subject to a 15% penalty for the first day. An additional 10% will be deducted for each additional day. Problem 1 (P1). The poultry farmer decided to make his own chicken scratch by combining alfalfa and corn in rail car quantities. A rail car of corn costs $400 and a rail car of alfalfa costs $200. The farmer's chickens have a minimum daily requirement of vitamin K (500 milligrams) and iron (400 milligrams), but it doesn't matter whether those elements come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of vitamin K and 50 milligrams of iron. Formulate the linear programming model for this situation and solve it using the graphical method. Problem 2 (P2). The international man of mystery knew the finest haberdashers the world over and constantly sought to expand his dazzling array of fine suits, ties, and cufflinks. Closet space was at a premium however, so purchases were carefully weighed. Each suit provides 23 units of dazzlement, each tie 14, and a set of cufflinks is worth an easy 8. A suit takes up 0.5 cubic feet of closet space and $900 of budget. A tie costs $135 and cufflinks cost $100 per set. Cufflinks are tiny even in the original box, they take up only .01 cubic feet while ties occupy a lusty .25 cubic feet. He has budgeted $12,000 for clothes on this trip and has 20 cubic feet of closet space left to fill. Formulate and solve the linear programming model for this situation. What would be the value of the objective function if the constraint S = 1 is added? Explain how you can determine the value without solving the revised problem. Problem 3 (P3). Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five different alternative excursions. In addition, the restaurant choices must be at least 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. A. Formulate and solve the linear programming model for this situation. B. Captain Stubing runs the LP model associated with the scenario and reads the following about the variable cells report. Provide an interpretation C. Using the Solution and Range Reports, provide as complete explanation about the Restaurant and Excursion portion. D. Using Solution and Range Reports, indicate which of Captain Stubing's limitations (RHSs) are reducing his profit. Problem 4 (P4): Target Shirt Company makes three varieties of shirts: Collegiate, Traditional and European. These shirts are made from different combinations of cotton and polyester. The cost per yard of unblended cotton is $5 and for unblended polyester is $4. Target can receive up to 4,000 yards of raw cotton and 3,000 yards of raw polyester fabric weekly. The table below pertinent data concerning the manufacture of the shirts. Shirt Collegiate Total Yards 1.00 Traditional 1.20 European .90 Fabric Requirement At least 50% cotton No more than 20% polyester Up to 80% polyester Weekly Contracts 500 Weekly Demand 600 Selling Price $14.00 650 850 $15.00 280 675 $18.00 TO DO: Develop and solve the linear programming model to maximize revenue. A. B. C. D. E. Define variables Objective function Constraints Bounds on variables Solution with its explanation