1) The Feed ‘N Ship feedlot fattens cattle for local farmers and ships them to meat markets in Kansas City and Omaha. The owners of the feedlot seek to determine the amounts of cattle feed to buy to satisfy minimum nutritional standards and, at the same time, minimize total costs. Each grain stock contains different amounts of four nutritional ingredients: A, B, C, and D. Here are the ingredient contents of each grain, in ounces per pound of grain.

The cost per pound of grains X,Y, and Z is $0.02, $0.04, and $0.025, respectively. The minimum requirement per cowper month is 64 ounces of ingredient A, 80 ounces of ingredient B, 16 ounces of ingredient C, and 128 ounces of ingredient D.

The feedlot faces one additional restriction. It can obtain only 500 pounds of stock Z per month from the feed supplier, regardless of its need. Because there are 100 cows at the Feed ‘N Ship feedlot at any given time, this constraint limits the amount of stock Z for use in the feed of each cow to no more than 5 pounds, or 80 ounces, per month.

2) MSA Computer Corporation manufactures two models of microcomputers, the Alpha and the Beta. The firm employs 5 technicians, working 160 hours each per month, on its assembly line. Management insists that full employment be maintained for each worker    (that is, all 160 hours of time) during next month’s operations. It requires 20 labor-hours to assemble each Alpha computer and 25 labor-hours to assemble each Beta model. MSA wants to see at least 10 Alpha’s and at least 15 Beta’s produced during the production period. Each Alpha generate $1,200 profit per unit whereas Beta’s yield $1,800 each. Determine the most profitable number of each model of microcomputer to produce during the coming month.