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Mathematically formulate a linear programming model

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PROBLEM- Dr. Konur selling Iphone 6 and Iphone 6+ Dr. Konur decided to sell new Iphones in Rolla. Particularly, he will sell Iphone 6 (i6) and Iphone 6+ (i6+).

Due to regulations, Dr. Konur can sell at most 50 Iphones in total per week and he wants to sell at least 25 Iphones in total per week. In a week, he should not sell more i6+ than i6 and he should not sell more than 25 i6's. From each i6, he makes a $50 profit; and, from each i6+, he makes a $50 profit. Dr. Konur wants to maximize his total weekly profit from iphone sales by determining how many Iphone 6 and Iphone 6+ to sell each week.

a) Mathematically formulate a linear programming model for Dr. Konur's Iphone sales problem. Define your decision variables and the notation you use for them, express the objective and objective function, and constraints using your decision variables. Combine everything to get the final linear model.

b) Solve Dr. Konur's problem using graphical method. Draw the axes, constraints, and determine the feasible region and the corner points. Then, find the optimum solution or optimum solutions. Does the model have infeasibility, unique optimum, alternative optima, or unboundedness?

c) Now suppose that Dr. Konur is allowed to sell more than 25 i6s per week. How does the feasible region change? Does the model have infeasibility, unique optimum, alternative optima, or unboundedness now? Explain briefly.

d) Now, addition to be allowed to sell more than 25 i6s per week, suppose that Dr. Konur can sell as many Iphones as he wants per week. How does the feasible region change?

Does the model have infeasibility, unique optimum, alternative optima, or unboundedness now? Explain briefly.


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