Question 1125890: APEX Company produces and sells three products: X, Y and Z. In order to produce them, the company needs to purchase four raw materials A, B, C and D. The prices of these four raw materials are $15/kg, $20/kg, $25/kg and $10/kg, respectively. Each month, the company has a limited budget of $50,000 to buy the raw materials. Producing one X requires 200g of A, 500g of C and 400g of D. Producing one Y requires 500g of A, 800g of B and 700g of C. Producing one Z requires 200g of A, 300g of B, 300g of C and 400g of D. The selling price of each product is based on the cost of raw materials: the profit margins of X, Y, and Z are 20%, 10%, and 25%, respectively.
From past historical data, the manager knows that due to economic situation, the monthly production of X and Z should be capped at 500 and 400 respectively. Besides, the monthly production of Y should be less than two third of the sum of the monthly production of X, Y and Z. Moreover, the monthly production of each product should be at least 100.
(a) Based on the given scenario above, develop a linear programming model to determine the optimal amount of products that the company should produce each month so that its profit is maximized. State your own assumptions and write the objective function and constraints clearly.
(b) Use Excel solver to solve the problem. Note down Answer Report and Sensitivity Report. Based on the report(s), identify the optimal solution and explain which constraints are binding and which are not.
(c) Interpret the sensitivity report from solver and discuss the following scenarios (without re-solving it using Excel Solver).
(i) If the monthly budget available is $80,000, how does it affect the optimal profit? If the monthly budget available is $30,000, how does it affect the optimal profit?
(ii) If the profit margin of Y becomes 15% and the profit margin of X becomes 12%, is there a change in the optimal solution?
(d) Discuss how changes in the budget and the selling prices will affect the company’s decisions and profit.
(Hint: you need to consider demand.)
Tips given:
1. There are 7 decision variables
2. There are 11 constraints
Please help! Thank you!
Answer by solver91311(24713)   (Show Source):
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