1306 Words6 Pages

TUTORIAL 2
Linear Programming - Minimisation Special cases Simplex maximisation
1. Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client’s needs. For a new client, Innis has been authorised to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%.
The client wants to minimise risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis’s risk measurement system, each unit*…show more content…*

Explain. b. If there are no feasible solutions, explain what is needed to produce 30 tons of fuel additive and 15 tons of solvent base. (ASW : Ch 2, Qn 48) 7. Reconsider the Kelson Sporting Equipment Inc example. Discuss the concepts of infeasibility, unbounded solution, and alternative optimal solutions as they occur in each of the following situations: a. Management has requested that the production of baseball gloves (regular model plus catcher’s model) be such that the total number of gloves produced is at least 750. That is, 1x1 + 1x2 > 750 b. The original problem has to be solved again because the profit contribution for the regular model is adjusted downward to $4 per glove. c. What would have to happen for this problem to be unbounded? (ASW : Ch 2, Qn 49) 8. Recall the Innis Investments problem. Letting x1 = units purchased in the stock fund x2 = units purchased in the money market fund leads to the following formulation: Min 8x1 + 3x2 s.t. 50x1 + 100x2 < 1,200,000 Funds available 5x1 + 4x2 > 60,000 Annual income x2 > 3,000 Units in money market x1, x2 > 0 Obtain and use the computer solution to answer the following: a. What is the optimal solution, and what is the minimum total risk? b. Specify the range of optimality for the objective function coefficients. c. How much annual income will be earned by the portfolio? d. What is the rate

Explain. b. If there are no feasible solutions, explain what is needed to produce 30 tons of fuel additive and 15 tons of solvent base. (ASW : Ch 2, Qn 48) 7. Reconsider the Kelson Sporting Equipment Inc example. Discuss the concepts of infeasibility, unbounded solution, and alternative optimal solutions as they occur in each of the following situations: a. Management has requested that the production of baseball gloves (regular model plus catcher’s model) be such that the total number of gloves produced is at least 750. That is, 1x1 + 1x2 > 750 b. The original problem has to be solved again because the profit contribution for the regular model is adjusted downward to $4 per glove. c. What would have to happen for this problem to be unbounded? (ASW : Ch 2, Qn 49) 8. Recall the Innis Investments problem. Letting x1 = units purchased in the stock fund x2 = units purchased in the money market fund leads to the following formulation: Min 8x1 + 3x2 s.t. 50x1 + 100x2 < 1,200,000 Funds available 5x1 + 4x2 > 60,000 Annual income x2 > 3,000 Units in money market x1, x2 > 0 Obtain and use the computer solution to answer the following: a. What is the optimal solution, and what is the minimum total risk? b. Specify the range of optimality for the objective function coefficients. c. How much annual income will be earned by the portfolio? d. What is the rate

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