(Solved):   Course: Operations Research 1 Topic: Linear Programming using Graphical Method Direction: ...

 

Course: Operations Research 1 Topic: Linear Programming using Graphical Method Direction: Analyze carefully the problems below, formulate the mathematical model and solve the problem using the graphical method. Maximization 1. The Flair Furniture Company produces inexpensive tables and chairs. The production process for each is similar in that both require a certain number of hours of carpentry work and a certain number of labor hours in the painting and varnishing department. Each table takes 4 hours of carpentry and 2 hours in the painting and varnishing shop. Each chair requires 3 hours in carpentry and 1 hour in painting and varnishing. During the current production period, 240 hours of carpentry time are available, and 100 hours in painting and varnishing time are available. Each table sold yields a profit of \( \$ 70 \); each chair produced is sold for a \( \$ 50 \) profit. 2. The two models of color TV sets produced by the Sekido Corp. will be designated as \( A \) and B. The company's aim is to maximize profit. The profit realized is \( \$ 300 \) from each model \( A \) and \( \$ 250 \) from each model B. Obviously, the more sets produced and sold, the better. The trouble is that there are certain limitations that prevent them from producing and selling thousands of sets daily. These limitations are: 1.Availability of only 40 hours of labor each day in the production dept. Each unit of model A requires two hours of labor, whereas each set of model B requires only one hour. (labor constraint) 2. A daily availability of 45 hours of machine time. Machine processing time for 1 unit of model A is 1 hour, and for 1 unit of model B, three hours. (machine constraint) 3. Inability to sell more than 12 sets of model A each day (marketing constraint) Minimization Problem 1. The Holiday Meal Turkey Ranch is considering buying two different brands of turkey feed and blending them to provide a good, low-cost diet for its turkeys. Each feed contains, in varying proportions, some or all of the three nutritional ingredients essential for fattening turkeys. Each pound of brand 1 purchased, for example, contains 5 ounces of ingredient A, 4 ounces of ingredient \( B \), and \( 0.5 \) ounces of ingredient \( C \). Each pound of brand 2 ccontains 10 ounces of ingredient \( A, 3 \) ounces of ingredient \( B \), but no ingredient \( C \). The brand 1 feed costs the ranch 2 cents a pound, while the brand 2 feed costs 3 cents a pound. The owner of the ranch would like to use \( \mathrm{LP} \) to determine the lowest-cost diet that meets the minimum monthly intake requirement for each nutritional ingredient. All ingredients must be at least 90 ounces, 48 ounces, and \( 1.5 \) ounces, respectively. 2. Jason is the Purchasing Manager of Kraft Foods, and he wants to determine the supply mix that will result in minimum cost. He can determine the data necessary for him to make a decision. A gallon of Alaska milk can produce 5 cases of cheese, 7 cases of butter, and 9 cases of cream. A gallon of Nestle milk can produce 11 cases of cheese, 8 cases of butter, and 4 cases of cream. He must produce at least 110 cases of cheeses, 112 cases of butter, and 72 cases of cream per day. Alaska milk costs \( \$ 50 \) per gallon, while Nestle milk costs \( \$ 55 \) per gallon.