The slack or surplus variables in each constraint

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A plumbing manufacturer makes two lines of bathtubs, model A and model B. Every tub requires blending a certain amount of steel and zinc; the company has available a total of 24,500 pounds of steel and 6,000 pounds of zinc. Each model A bathtub requires a mixture of 120 pounds of steel and 20 pounds of zinc, and each yields a profit of $90. Each model B tub produced can be sold for a profit of $70; it requires 100 pounds of steel and 30 pounds of zinc. To maintain an adequate supply of both models, the manufacturer would like the number of model A tubs made to be no more than 5 times the number of model B tubs. Find the best product mix of bathtubs.

Please answer the following questions without using excel.

(Note: In this problem, replace the word “profit” with “price”, so that the goal of the company is to find the best product mix that maximizes revenue.)

1) Formulate the LP problem.

2) Provide the graphical solution to this problem following the procedure discussed in class.

Note: make sure you draw the objective function in your graphical solution.

3) At the optimal solutions your have solved in 2), calculate the values of RHS and LHS and the slack or surplus variables in each constraint. Provide an economic interpretation for each non-zero slack or surplus value.

4) Suppose the price of model B increases to $80, what is the new objective function and new optimal solution?

Reference no: EM132221793

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