Industrial Operations Analysis

Linear Programming Model Formulation: Formulate a Linear Programming model for each problem below, and solve it using Graphical Method and computer software LINGO. 1. Al Hammad manufacturing company is introducing two new lightweight bicycle frames, the Deluxe and the Professional, to be made from aluminum and steel alloys. The expected unit profits are SAR 20 for the Deluxe and SAR 40 for the Professional. The number of pounds of each alloy needed per frame is summarized in the following table. A supplier delivers 18 pounds of the aluminum alloy and 18 pounds of the steel alloy weekly Table: Pounds of each alloy needed per frame Frame Aluminum Alloy Steel Alloy Deluxe 2 3 Professional 3 2 How many Deluxe and Professional frames should Al Hammad manufacturing company produce each week? 2. A candy manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock. He decides to sell them in the form of two different mixtures. One mixture will contain half cherries and half mints by weight and will sell for SR 2.00 per pound. The other mixture will contain one-third cherries and two-thirds mints by weight and will sell for SR1.25 per pound. How many pounds of each mixture should the candy manufacturer prepare in order to maximize his sales revenue? 3. Al Mansoori firm produces two types of refrigerators: Type-A and Type-B. There are two production lines. The first line is dedicated to produce refrigerators of Type-A. The other one is delectating to produce refrigerators of the Type-B. The production capacity of the first line is 70 units per day, and that of the second line is 60 units per day. The product of Type-A requires 20 minutes of labor time where Type-B requires 40 minutes. Presently, there is a maximum of 40 hours of available labor time per day which can be assigned to either of the production lines. The profit contribution of Type-A is SR 30 per refrigerator produced and that of Type-B is SR 40 per product produced. Obtain the optimal production mix that will maximize the total profit contribution