Consider the linear programming problem: Maximize P : 60512 + 503; . m-i-ySSO 5m+10yg560 50$+20y S 1600 51220 3120 Use the simplex method to solve the problem. Use 5, t, and u as your slack variables for the first, second, and third inequalities respectively. Use the final simplex tableau to identify the values below. X: Using the information below to create the initial simplex matrix. Assume all variables are nonnegative. Maximize f : 53:1 + 3:32 subject to 4331 + 21122 S 45 8:31 + 7332 S 45 $120 $220 A farmer has a field of 70 acres in which he plants potatoes and corn. The seed for potatoes costs 520/ acre, the seed for corn costs 560/ acre, and the farmer has set aside $3000 to spend on seed. The profit per acre of potatoes is $150 and the profit for corn is $50 an acre. How many acres of each should the farmer plant? acres of potatoes acres of corn What is the maximum profit? S Using the information below to create the initial simplex matrix. Assume all variables are nonnegative. Maximize f = 8m + 53:2 subject to 5561 + 31132 S 70 3371 + 7332 S 50 13120 $220 Consider the linear programming problem: Maximize P z 103: + 40y . 233+ y S 100 80:12 + 10y g 500 30:: + 103; S 2000 $2 0 yZO Use the simplex method to solve the problem. Use 5, t, and u as your slack variables for the first, second, and third inequalities respectively. Use the final simplex tableau to identify the values below. x: Using the information below to create the initial simplex matrix. Assume all variables are nonnegative. Maximize f : 7m + 43:2 subject to 11931 + 41132 S 45 23:1 + 103:2 S 50 13120 13220 Using the information below to create the initial simplex matrix. Assume all variables are nonnegative. Maximize f = 8w1 + 63:2 + 41:3 subject to 41171 + 51172 + 2273 S 45 9.171 + 2932 + 8173 S 55 8171 + 6172 + 5273 S 65 1131 2 0 132 Z 0 333 Z 0