Question

Question 4. The Jean-Pierre Amor Company manufactures two lines of designer yard gates, called model A and model B. Every gate requires blending a certain amount of steel and zinc; the company has available a total of 25,000lb of steel and 6,000lb of zinc. Each model A requires a mixture of 150lb of steel and 20lb of zinc, and each yields a profit of $90. Each model B gate requires 100lb of steel and 30lb of zinc and can be sold for a profit of $70. Formulate an LP for this problem to find the best production mix of yard gates by answering the questions below. What are the decision variables? How many decision variables are there? Clearly explain the decision variables in English and provide the mathematical notation used in the algebraic formulation of the decision problem b) What is the objective function? Clearly explain the objective function in English and provide the mathematical formulation. c) What are the constraints of the problem? Clearly explain each constraint in English and provide the mathematical formulation. d) Are there any sign or type restrictions in your formulation? Why or why not? Clearly explain the sign and type restrictions (if any).

Answer 1

a) There are two decision variables here , i.e the number of units of Model A to be made = x1 and the number of units of Model B to be made = x2

b)So, the decision here is to maximize the profit by making an optimum mix of Model A and Model B.

So, let the profit function or objective function be Z , so Z = 90 * x1 + 70 * x2 , because each unit of model A gives a profit of $90 and each unit of model B gives a profit of $70.

Mathematical formulation = Z = 90 * x1 + 70 * x2 ,

c)The constarints in this case is the availability of Zinc and Steel.

So , Zinc Availability Constraint: - 20 *x1 + 30*x2 < = 6000 which means that the total amount of Zinc consumed after making the models should be less than or equal to 6000lbs

So , Steel Availability Constraint: - 150 *x1 + 100*x2 < = 25000 which means that the total amount of steel consumed after making the models should be less than or equal to 25000lbs

d) There is a restriction of the sign of using less than or equal to because the amount of material consumed can be more than . the quantity available.

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