1. A Singapore company manufactures 50-inch and 75-inch rear projection television sets. Each 50-inch set contributes $200 to profits and each 75-inch set contributes $475 to profits. The company has purchase commitments for 500 50-inch sets and 200 75-inch sets for the next month so they want to make at least that many. Although they think they can sell all the 50-inch sets that they could currently make, they do not think they can sell more than 375 75-inch sets. Their factory capacity allows them to make only 975 sets of both sizes total. Formulate as a linear programming problem.
2. National Credit Union has $200,000 available to invest in a 12-month commitment. The money can be placed in Treasury notes yielding an 6 % return or municipal bonds yielding an average rate of return of 8 %. Credit union regulations require diversification to the extent that no more 30% of the investment be placed in Treasury notes. Because of defaults in such municipalities as Cleveland and New York, it is decided that at least 20% of the investment be place in bonds. Formulate as a linear programming problem.