ENGG-6140: Engineering Assignment Help

Assignment Task

1. (Ch3 Textbook Prob. 3-27) Consider the two-dimensional solution space in Figure below

1. Suppose that the objective function is given as Maximize z = 6x1 + 3x2 If the simplex iterations start at point A, identify the path to the optimum point D.
2. Determine the entering variable, the corresponding ratios of the feasibility condition, and the change in the value of z, assuming that the starting iteration occurs at point A and that the objective function is given as Maximize z = x1 + 4 x2

2. (Ch3 Textbook Prob. 3-31) The Gutchi Company manufactures purses, shaving bags, and backpacks. The construction includes leather and synthetics, leather being the scarce raw material. The production pro- cess requires two types of skilled labor: sewing and finishing. The following table gives the availability of the resources, their usage by the three products, and the profits per unit.

a) Formulate the problem as a linear program and find the optimum solution (using Simplex).

b) From the optimum solution, determine the status of each resource.

3. (Ch3 Textbook Prob. 3-71) A company that operates 10 hrs a day manufactures three products on three processes. The following table summarizes the data of the problem:

a) Determine the optimal product mix.

b) Use the dual prices to prioritize the three processes for possible expansion

c) If additional production hours can be allocated, what would be a fair cost per additional hour for each process?

4. (Ch3 Textbook Prob. 3-77) Using your solution to Q2 in this Assignment (Ch3 textbook Prob. 3.31) indicate whether the following changes in the resources will keep the current solution feasible and, For each case where feasible is maintained, determine the new optimum solution (values of the variables and the objective function)

a) Available leather is increased to 45 ft²

b) Available leather is decreased by 1 ft²

c) Available sewing hours are changed to 38 hours

d) Available sewing hours are changed to 46 hours

e) Available finishing hours are decreased to 15 hours

f) Available finishing hours are increased to 50 hours

g) Would you recommend hiring an additional suing worker for $15 dollars an hour

5. (Ch3 Textbook Prob. 3-84) The Bank of Elkins is allocating a maximum of $200,000 for personal and car loans during the next month. The bank charges 14% for personal loans and 12% for car loans. Both types of loans are repaid at the end of a 1-year period. Experience shows that about 3% of personal loans and 2% of car loans are not repaid. The bank usually allocates at least twice as much money to car loans as to personal loans.

a) Determine the optimal allocation of funds between the two loans and the net rate of return on all the loans.

b) If the percentages of personal and car loans are changed to 4% and 3% respectively, use sensitivity analysis to determine if the optimum solution in (a) will change

5. (Ch4 Textbook Prob. 4-1 and 4-2) Find the dual problem for each of the following primal problem

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