C03 p19-32 LP 12ed

C03 p19-32 LP 12ed - Chapter 3 Linear Programming...

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Chapter 3 Linear Programming: Sensitivily Analysis and Interpretation of Solution 19. Better Products, Inc., manufactures three products on two machines. In a typical w 40 hours are available on each machine. The profit contribution and production time hours per unit are as follows: Wegwp""2 "*I . [email protected]& B .prow&- ' . &3Q - . . .. .-$$o. . Machine 1 timelunit . 0.5 2.0 I , MpeMe 2 timdrmit '. 1:O' . 1.6' - u - ired for machine 1; thus, 2 hours of lab& &"s't be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 100 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 20% of the units produced. a. How many units of each product should be produced to maximize the total profit con- tribution? What is the projected weekly profit associated with your solution? b. How many hours of production time will be scheduled on each machine? c. What is the value of an additional hour of labor? d. Assume that labor capacity can be increased to 120 hours. Would you be interested in using the additional 20 hours available for this resource? Develop the optimal prod- uct mix assuming the extra hours are made available. 20. Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans. a. Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan in order to maximize the total annual return for the new funds. b. How much should be allocated to each type of loan? What is the total annual return? What is the annual percentage return? c. If the interest rate on home loans increased to 9%, would the amount allocated to each type of loan change? Explain. d. Suppose the total amount of new funds available was increased by $10,000. What ef- fect would this have on the total annual return? Explain. e. Assume that ASB has the original $1 million in new funds available and that the plan- ning committee has agreed to relax the requirement that at least 40% of the new funds must be allocated to home loans by 1%. How much would the annual return change? How much would the annual percentage return change? 21. Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Rental Class I Deluxe Business $35 - 'ope 11 $20 $30 $40 . - r , ' , > , Type I rooms do not have Internet access and are not available for the Business rental class.
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