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Solutions to Lp Problems

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Solutions to LP Practice Problems[1] 1. Furnco manufactures desks and chairs. Each desk uses 4 units of wood, and each chair uses 3 units of wood. A desk contributes $40 to profit, and a chair contributes $25. Marketing restrictions require that the number of chairs produced be at least twice the number of desks produced. There are 20 units of wood available. Using the graph below, determine a production plan that maximizes Furnco’s profit. a) Draw isoprofit lines where the total profit equals 125, 150, 175, and 200. Here are the points where the isoprofit lines cross the axes: | |X1 |X2 | |z = 125 |0 |5 | | |3.125 |0 | |z = 150 |0 |6 | | |3.75 |0 | |z = 175 |0 …show more content…

Cells E13:E16 in the answer report indicate that we should invest 25% of the funds in each of the four types. b) What is the expected return on investment from the optimal portfolio? From cell E8 in the answer report, the optimal portfolio will return 14.75% ($73,750). c) What would be the improvement in the return on investment if the limit on the total amount invested in personal loans were increased to 30%? We look at cell E20 in the Sensitivity Report, and see that the shadow price is 1%. That means that for every unit of increase in this constraint’s right-hand side, we will realize a 1% improvement in the objective function. If we change the right-hand side of this constraint from 25% to 30% (a change that is within the allowable increase shown in cell G20 of the Sensitivity Report), then the objective function will increase by 0.05 * 0.01 = 0.0005. Our portfolio return would go from 0.1475 to 0.1480 (from 14.75% to 14.80%). d) If the return on bonds increases from 10% to 13%, what will happen to the optimal allocation of funds? Cell G9 in the Sensitivity Report indicates that the bond return would have to increase by at least 4.5% before the optimal investment mix would change. Since this is only a 3% increase, the portfolio would not change (although it would become more profitable). 4. Sunco Oil manufactures three types of gasoline (gas 1, 2, and 3). Each

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