Information: A student is given a bag containing 6 large Legos and 9 small Legos
ID: 2972181 • Letter: I
Question
Information: A student is given a bag containing 6 large Legos and 9 small Legos. The Legos can be used to make tables, chairs and benches. Each table requires two large Legos and two small Legos. Each chair requires one large Lego and two small Legos. Each bench requires one large Lego and one small Lego. Suppose that the price of the tables is $16, the price of chairs is $10 and the price of benches is $9 and that the objective is to maximize revenue. Question: Define the decision variable and give the objective function in terms of the variables.Explanation / Answer
mathematical approach to the problem of allocating limited resources among competing activities in an optimal manner. Specifically, it is a technique used to maximize revenue, Contribution Margin (CM), or profit function or to minimize a cost function, subject to constraints. Linear programming consists of two important ingredients: (1) objective function and (2) constraints, both of which are linear. In formulating the LP problem, the first step is to define the decision variables that one is trying to solve. The next step is to formulate the objective function and constraints in terms of these decision variables. For example, assume a firm produces two products, A and B. Both products require time in two processing departments, assembly and finishing. Data on the two products are as follows: Products A B Available Assembly (hours) 2 4 100 Finishing (hours) 3 2 90 CM/unit $25 $40 The firm wants to find the most profitable mix of these products. First, define the decision variables as follows: A = the number of units of product A to be produced B = the number of units of product B to be produced Then, express the objective function, which is to maximize total contribution margin (TCM), as: TCM = $25A + $40B Formulate the constraints as inequalities: 2A + 4B < 100 3A + 2B < 90 and do not forget to add the non-negative constraints: Source: http://www.allbusiness.com/glossaries/decision-variable/4952417-1.html#ixzz2IGCv6yUQ