Optimization Modeling Questions

ninen620
timer Asked: Mar 6th, 2016

Question Description

Please take a look at the homework formatting instructions PDF and template and apply those guidelines to answer the four questions in the "Assignment" file. There is also an accompanying Excel spreadsheet. Thank you!

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Glickman Electronics Example The Glickman Electronics Company in Washington, DC, produces two products: (1) the Glickman x-pod, a portable music player, and (2) the Glickman BlueBerry, an internet-connected color telephone. The production process for each product is similar in that both require a certain number of hours of electronic work and a certain number of labor-hours in the assembly department. Each x-pod takes 4 hours of electronic work and 2 hours in the assembly shop. Each BlueBerry requires 3 hors in electronics and 1 hour in assembly. During the current production period, 240 hours of electronic time are available, and 100 hours of assembly department time are available. Each x-pod sold yields a profit of $7; each BlueBerry produced may be sold for a $5 profit. Glickman’s problem is to determine the best possible combination of x-pod and BlueBerrys to manufacture to reach the maximum profit. Solution: a. Formulate the problem as a linear programming model (that is, define the variables, and write down the objective function and all constraints mathematically). We begin by summarizing the information needed to formulate and solve this problem. Further, let’s introduce some simple notation for use in the objective function and constraints. Decision Variables X1 = number of x-pods to be produced X2 = number of BlueBerry to be produced Objective Function and constraints Max ($7X1 + $5X2) Subject to: 4X1 + 3X2 ≤ 240 2X1 + 1X2 ≤ 100 X1 , X2 ≥ 0 The objective function created this way represents the overall profit from the operation. Since each x-pod yields a profit of $7, X1 of them yield 7X1 dollars. Similarly, each BlueBerry yields a profit of $5, which means X2 BlueBerrys yield 5X2 dollars. The overall profit will therefore be = $7X1 + $5X2, which is the objective function we are trying to maximize. As for the constraints, one general relationship is that the amount of a resource used is to be less than or equal to the amount of resource available. Both these constraints represent production capacity restrictions and, of course, affect the total profit. First constraint: Electronic time used is ≤ Electronic time available. Second constraint: Assembly time used is ≤ Assembly time available. For example, Glickman Electronics cannot produce 70 x-pods during the production period because if X1 = 70, both constraints will be violated. It also cannot make X1 = 50 x-pods and Xx = 10 BlueBerrys. What is more, since the decision variables represent units of production, we should add a nonnegativity constraint for each variable. b. Create a spreadsheet model for this problem and solve with Excel Solver. Figure 1 - Solver parameters A 1 2 3 4 5 Production Electronic Constraint Assembly Constraint Objective Function (Maximization) B X-PODS (X1) 30 4 2 C BLUEBERRYS (X2) 40 3 1 7 5 D E F 240
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