# All solutions

Identify the feasible region for the following set of constraints:
2A – 1B <= 0
-1A + 1.5B <= 200
A, B >= 0

George Johnson recently inherited a large lum 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 option: (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 he finally decides o commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 7.5%.

1.) Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives.

2. Solve the problem using the graphical solutions procedure

AutoIgnite produces electronic ignition systems for automobiles at a plant in Cleveland, Ohio. Each ignition system is assembled from two components produced at AutoIgnite’s plants in Buffalo, New York, and Dayton, Ohio. The Buffalo plant can produce 2000 units of component 1, 1000 units of component 2, or any combination of the two components each day. For instance, 60% of Buffalo’s production time could be used to produce component 1 and 40% of Buffalo’s production time could be used to produce component 2; in this case, the Buffalo plant would be able to produce 0.6(2000) = 1200 units of component 1 each day and 0.4(1000) = 400 units of component 2 each day. The Dayton plant can produce 600 units of component 1, 1400 units of component 2, or any combination of the two components each day. At the end of each day, the component production at Buffalo and Dayton is sent to Cleveland for assembly of the ignition systems on the following work day.

a. Formulate a linear programming model that can be used to develop a daily production schedule for the Buffalo and Dayton plants that will maximize daily production of ignition systems at Cleveland.

b. Find the optimal solution.

c. Find the optimal solutions.