2-4 **LINEAR PROGRAMMING PROBLEMS****1. Feed Purchase Optimization:**A laboratory needs two types of feed, A and B, for its animals. - **Feed A:** - Carbohydrates: 2 units/pound - Protein: 4 units/pound - Cost: $1.40/pound - **Feed B:** - Carbohydrates: 8 units/pound - Protein: 2 units/pound - Cost: $1.60/poundThe lab requires a minimum of 80 units of carbohydrates and 132 units of protein. Determine the pounds of each feed to purchase to minimize costs. _Solution: 32 units of feed A and 2 units of feed B; Minimum Cost: $48_**2. Printer Production Optimization:**Evergreen Company produces two printer types: Inkjet and Laserjet.- Maximum capacity: 120 printers/day- Labor: 400 hours/day- Inkjet: - Time: 2 hours/printer - Profit: $80- Laserjet: - Time: 6 hours/printer - Profit: $120How many of each printer should be produced to maximize profits?_Solution: 80 Inkjet, 40 Laserjet; Max. Profit = $11,200_**3. Chip Production Optimization:**A company manufactures two chip types: one at 2.0 GHz, the other at 2.8 GHz.- Max production: - Fast Chips: 50/day - Slow Chips: 100/day- Labor: 360 hours/day- Fast Chip: - Time: 6 hours/chip - Profit: $20- Slow Chip: - Time: 3 hours/chip - Profit: $27Determine the quantity of each chip type to maximize profit._Solution: 10 fast chips and 100 slow chips_**4. Feed Purchase Optimization (Variant):**A laboratory requires two types of feed, A and B, for its animals.- **Feed A:** - Carbohydrates: 2 units/pound - Protein: 4 units/pound - Cost: $1.40/pound - **Feed B:** - Carbohydrates: 6 units/pound - Protein:

LINEAR PROGRAMMING PROBLEMS 1. A laboratory wishes to purchase two different types of feed, A and B, for its animals. Type A feed has 2 units of carbohydrates per pound and 4 units of protein per pound. Type B feed has 8 units of carbohydrates per pound and 2 units of protein per pound. Feed A costs 1.40 per pound and feed B costs 1.60 per pound. If at least 80 units of carbohydrates and 132 units of protein are required, how many pounds of each feed are required to minimize the cost? What is the minimal cost? (32 units of feed A and 2 units of feed B; Minimum Cost: $48) 2. Evergreen Company produces two types of printers, Inkjet and Laserjet. The company can make at most 120 printers per day and has 400 labor-hours available per day. It takes 2 hours to make the Inkjet and 6 hours to make the Laserjet. If the profit on the Inkjet is $80 and profit on the Laserjet is $120, find how many of each printer to yield the maximum profit and the maximum profit. (80 Inkjet, 40 Laserjet; Max. Profit = $11,200) 3. A company manufactures two types of computer chips, one that runs at 2.0 GHz and the other that runs at 2.8 GHz. The company can make a maximum of 50 fast chips and 100 slow chips per day. It takes 6 hours to make a fast chip and 3 hours to make a slow chip, and the employees can provide up to 360 hours of labor per day. The company makes a profit of $20 on each fast chip and $27 on each slow chip. How many of each should be made to maximize profit? List the maximum profit. (10 fast chips and 100 slow chips) 4. A laboratory wishes to purchase two different types of feed, A and B, for its animals. Type A feed has 2 units of carbohydrates per pound and 4 units of protein per pound. Type B feed has 6 units of carbohydrates per pound and 2 units of protein per pound. Feed A costs 1.40 per pound and feed B costs 1.60 per pound. If at least 30 units of carbohydrates and 40 units of protein are required, how many pounds of each feed are required to minimize the cost? What is the minimal cost? (9 units of A and 2 units of B; Minimum Cost: $15.80)