CPSMA 3933 - Operations and Market Research - LP Model Optimum Solution - Operations Assignment Help

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CPSMA 3933 -  Operations and Market Research - LP Model Optimum Solution - Operations Assignment Help

1. A company produces two products, A and B. The sales volume for A is at least 80% of the total sales of both A and B. However, the company cannot sell more than 100 units of A per day. Both products use one raw material, of which the maximum daily availability is 240Ib. The usage rates of the raw material are 21b per unit of A, and 4Ib per unit of B. The profit units for A and B are $20 and $50, respectively. Determine the optimal product mix for the company using Solver. Save the table and solution in a separate Excel sheet within the same Excel file.
2. An individual wishes to invest $5000 over the next year in two types of investment: Investment A yields 5%, and investment B yields 8%. Market research recommends an allocation of at least 25% in A and at most 50% in B. Moreover, investment in A should be at least half the investment in B. How should the fund be allocated to the two investments? Find the optimal solution using Solver. Save the table and solution in a separate Excel sheet within the same Excel file.
3. Four products are processed sequentially on three machines. The following table gives the pertinent data of the problem.
Manufacturing time (hr) pe unit

Formulate the problem as an LP model and find the optimum solution using Solver. Save the table and solution in a separate Excel sheet within the same Excel file. —15 points
4. Consider the following set of constraints: + 2x2 + 2x3 + 4x4 A 40
2x1 — x2 + x3 + 2x4 A 8
4x1 — 2x2 + x3 — x4 10 X1,xz,X3,X4 > 0 Solve the problem for each of the following objective functions using Solver. Save the table and solution in a separate Excel sheet within the same Excel file for each part (4 separate sheets for this problem).
(a) Maximize z = 2x1 + x2 — 3x3 + 5x4 (b) Maximize z = 8x1 + 6x2 + 3x3 — ara (c) Maximize z = 3x1 — x2 + 3x3 + 4x4 (d) Maximize z = 5x1 — 4x2 + 6x3 — 8x4 5. Solve the dual of the following problem. Save the table and solution in a separate Excel sheet within the same Excel file.
Minimize z = 5x1 + 6x2 + 3x3
Subject to:
5x1 + 5x2 + 3x5 50 x, + x3 20 7x1 + 6x2 — 9x3 30 5x1 + 502 + 5x3 35 2x1 + 4x2 — 15x3 10 12x1 + 10x2 90 x2 — 10x3 20
Xi, X2, X3 U 0

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