Case Study Mat540 Extra Credit: Linear Programming (Essay Sample)

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Case Study Mat540 Extra Credit
Introduction
A linear programming model is a constituent of several constraints together with an objective function designed to solve it to obtain the optimum quantities. In linear programming, a constraint is also referred to as a variable with which the objective function is correlated. For instance, solving of linear programming models (LP) can either be maximizing or minimizing them depending on the nature of the problem (William, 1999). Costs of production are always minimized whereas the profits should be maximized subject to some given variables or the constraints. In other words, some constraints cannot be negative, for example, production of chairs in firms. That calls for the non-negativity constraint that is also included in formulating the LP models.
5a. The company is interested in minimizing the cost of producing the ounces; hence, this is a minimizing problem of linear programming. Arranging the variables gives a situation shown below,
VariableNPhPCost($)1106-322615Projected20362-The LP model can be formulated as follows as we let the number of pounds used to produce fertilizer in the Kola Company using chemical 1 and 2 to be X and Y respectively;
Min. C= QUOTE


Subject to






X, Y ≥0
6a. This Pinewood Company is interested in maximizing the profit from production of chairs and tables. If we let the number of chairs to be produced to be X and that of tables to be Y, then a LP model can be formulated as follows;
Variable
Chairs
Tables
Profit($)
Labor
8
10
400
Wood
2
6
100
Projected
80
36
-
LP becomes
Max. R=
St.
X,Y ≥0
9a. To make a cake and a Danish product, this firm can let the number of cakes, and that of Danish to be X and Y respectively s that .
Variable
Flour
Sugar
Profit($)
Cakes
5
2
1
Danish
5
4
5
Projected
25
16
-
The LP is as follows;
Max T=
St.
X,Y ≥0
12a. The Elixer Drug Company will have to formulate a good model in order to find the optimum number of drugs that can be manufactured using the three ingredients;
Using the table below, a possible model can be formulated to help this company find optimum quantities to produce using the three ingredients respectively,
VariableIngredient 1Ingredient 2Ingredient 3CostX31280Y11660Projected6412
Min. C= QUOTE








X, Y≥0
13a. The jewelry store will be maximizing the outcome from the production of bracelets and necklaces using the ounces that are a...