Problem 3. A certain plant can manufacture five different products in any combination. Each product requires time on each of three machines in the following manner (all figures in minutes/unit: Product Machine 2 1 3 A 12 8 5 B 7 9 10 8 4 7 D 10 0 3 E 7 11 2 Each machine is available 128 hours per week. Products A, B, and Care purely competitive, and any amounts made may be sold at respective prices of $5, $4, and $5. The first 20 units of D and E produced per week can be sold at $4 each, and all made in excess of 20 can only be sold at $3 each. Variable labor costs are $4 per hour for machines 1 and 2 and $3 per hour for machine 3. Material costs are $2 for products A and C and $1 for products B, D, and E. Formulate the problem to maximize profit for the firm. Use Solver*** Problem 3. A certain plant can manufacture five different products in any combination. Each product requires time on each of three machines in the following manner (all figures in minutes/unit: Machine Product 1 3 A 5 12 7 2 8 9 4 B 10 C 8 D 10 0 11 7 3 2 E 7 Each machine is available 128 hours per week. Products A, B, and Care purely competitive, and any amounts made may be sold at respective prices of $5, $4, and $5. The first 20 units of D and E produced per week can be sold at $4 each, and all made in excess of 20 can only be sold at $3 each. Variable labor costs are $4 per hour for machines 1 and 2 and $3 per hour for machine 3. Material costs are $2 for products A and Cand $1 for products B, D, and E. Formulate the problem to maximize profit for the firm