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##### EMGT501 Week Assignment Problems Solution

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solution

**Question**

11. Solve the following linear program using the graphical solution procedure;Max 5A + 5B;s.t.;1A < 100 (Less than or equal to is the sign);1B < 80 (Less than or equal to is the sign);2A + 4B 0 (Greater than or equal to is the sign);Production Time (hours);Cutting Inspection Profit;and and per;Product Dying Sewing Finishing Packaging Bag;Standard 7/10 1/2 1 1/10 $10;Deluxe 1 5/6 2/3 1/4 $9;15. Suppose that Par's management (Problem 14) encounters the following situation;a. The accounting department revises its estimate of the profit contribution for the deluxe bag to $18 per bag.;B. A new lost-cost material is available for the standard bag, and the profit contribution per standard bag can increased to $20 per bag. (Assume that the profit contribution of the deluxe bag is the original $9 value.);c. New sewing equipment is available that would increase the sewing operation capacity to 750 hours. (Assume that 10A + 9B is the appropriate objective function.);If each of these situations is encountered separtely, what is the optimal solution and the total profit contribution?;23. Embassy Motorcycles (EM) manufacturers two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders. Embassy produces the engines for both models at its Des Moines, Iowa, plant. Each EZ-Rider engine requires 6 hours of manufacturing time and each Lady-Sport engine requires 3 hours of manufacturing time. The Des Moines plant has 2100 hours of engine manufacturing time available for the next production period. Embassy's motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex and the supplier can only provide up to 280 Lady-Sport frames for the next production period. Final assembly and testing requires 2 hours for each EZ-Rider model 2.5 hours for each Lady-Sport model. A maximum of 1000 hours of assembly and testing time are available for the next production period. The company's accounting department projects a profit contribution of $2400 for each EZ-Rider produced and $1800 for each Lady-Sport produced.;a. Formulate a linear programming model that can be used to determine the number of units of each model that should be produced in order to maximize the total contribution to profit.;b. Solve the problem graphically. What is the optimal solution?;c. Which constraints are binding?;Production Time (hours);Cutting Packaging;Model and Sewing Finishing and Shipping Profit/Glove;Regular model 1 1/2 1/8 $5;Catcher's model 3/2 1/3 1/4 $8;25. George Johnson recently inherited a large sum of money, he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond form. In addition, he wants to select a mix that will enable him to obtain a total return of at least 7.5%.;a. Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives.;b. Solve the problem using the graphical solution procedure.;Standard Grade Professional Grade;Fiberglass 84% 58%;Carbon fiber 10% 30%;Kevlar 6% 12%;39. 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 authorized 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 costs $100 and provides an annual rate of return of 4%. The client wants to minimize 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 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 fund simply indicates that it is riskier investment. Innis's client also specifies that at least $300,000 be invested in the money market fund.;a. Determine how many units of each fund Innis should purchase for the client to minimize the total risk index for the portfolio.;b. How much annual income will this investment strategy generate?;c. Suppose the client desires to maximize annual return. How should the funds be invested?

Paper#23524 | Written in 18-Jul-2015

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