The client wants to minimize risk subject to the requirement that the annual income from the investment he at least $60,000. According to Inning’s risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3; the higher risk index associated with the stock tune simply indicates that it is the riskier investment. Inning’s client has also specified that at least $300,000 be invested in the money market fund.
A. Determine how many units of each fund Inns should purchase for the client to minimize the total risk index for the portfolio. . How much annual income will this investment strategy generate? . Suppose the client desires to maximize annual return. How should the funds be invested? (SAW: Chi 2, CNN 37 – Inns – mill) 2. Photo Chemicals produces two types of photographic developing fluids.
Both products cost Photo Chemicals SSL per gallon to produce. Based on an analysis of current inventory levels and outstanding orders for the next month, Photo Chemicals’ management has specified that at least 30 gallons of product 1 and at least 20 gallons to product 2 must be produced during the next 2 weeks.
Management has also stated that an existing inventory of highly perishable raw trial required in the production to both fluids must be used within the next 2 weeks. The current inventory of the perishable raw material is 80 pounds. While more of this raw material can be ordered if necessary, any of the current inventory that is not used within the next 2 weeks will spoil – hence, the management requirement that at least 80 pounds be used in the next 2 weeks. Furthermore, it is known that product I requires I pound of this perishable raw material per gallon and product 2 requires 2 pounds of the raw material per gallon.
Since Photo Chemicals’ Objective is to keep its production costs at he minimum possible level, the firm’s management is looking for a minimum- cost production plan that uses all the 80 pounds Of perishable raw material and provides at least 30 gallons of product 1 and at least 20 gallons of product 2. What is the minimum-cost solution? (SAW: Chi 2, CNN 38 – Photo ; min) 3. Does the following linear program involve infeasibility, unbounded, and/or alternative optimal solutions? Explain. Max ex. ex. ex. 4 ex. < 10 -Ixi + lx2>8 XSL, xx>0 (SAW Chi 2, CNN 40 – infeasible) 4.
Does the following linear program involve infeasibility, unbounded, and/or alternative optimal solutions? Explain Max Xix *lax ex. * ex. > 24 ex.>4 (SAW : Chi 2, CNN 41 – unbounded) 5. Reconsider the ARM situation. A. Identify all the extreme points of the feasible region. B. Suppose ARM discovers away to increase the profit of solvent base to $60 per ton, Does this change the optimal solution? If so, how? C. Suppose the profit for the solvent base is SO per ton, What is the optimal solution now?
Comment on any special characteristics that may exist with this profit for the solvent base. Chi 2, CNN 47) 6. Reconsider the ARM situation. Suppose that management adds the acquirement that at least 30 tons of fuel additive and at least 15 tons of solvent base must be produced. A. Graph the constraints for this revised ARM problem. What happens to the feasible region? 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. : Chi 2, CNN 48) 7.
Reconsider the Keelson Sporting Equipment Inc example. Discuss the concepts of infeasibility, unbounded solution, and alternative optimal solutions as they occur in each tooth following situations: a. Management has requested that the production of baseball gloves (regular del plus catcher’s model) be such that the total number of gloves produced is at least 750. That is, Xix +ex.> 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? : Chi 2, CNN 49) . Recall the Inns Investments problem. Letting XSL = units purchased in the stock fund xx units purchased in the money market fund leads to the following formulation: Min ex. + ex. xx + xx Funds available SKI ex. > 60,000 Annual income xx 3,000 Units in money market 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. . How much annual income will be earned by the portfolio? D. What is the rate of return for the portfolio? E. What is the dual price for the funds available constraint? F. What is the marginal rate of return on extra funds added to the portfolio? (SAW: Chi 3, CNN 16 – TM’S – min) 9. Refer to the Inns Investments example and the computer output from the TM’S analysis: a. Suppose the risk index for the stock fund (the value of CLC) increases from its current value of 8 to 12. How does the optimal solution change, if at all?
Suppose the risk index for the money market fund (the value of co) increases from its current value of 3 to 3. 5. How does the optimal solution change, if at all? C. Suppose CLC increases to 12 and co increases to 3. 3. How does the optimal solution change, if at all? (SAW: Chi 3, CNN 17) 10. Solve the following linear program using the graphical approach: Maxima ex. ex. 4 ex. < 20 3×1 + 7×2 put the linear program in tableau form, and solve using the simplex method, Show the sequence ot extreme points generated by the simplex method on your graph, (ASW: Ch5, Qn 7 -simplex – max) 11.
Recall the problem for Par Inc (Book Section 2. 1). The mathematical model for this problem, is restated below: Max xx + ex. [pick]XSL * Ski 630 Cutting and dyeing [apical + [pick]xx 600 Sewing Xix * [pick]k 708 Finishing [apical * [pickax 135 Inspection and packaging where XSL number of standard bags produced xx = number of deluxe bags produced a, use the simplex method to determine how many bags of each model Par should manufacture? B. What is the profit Par can earn with these reduction quantities?