2. A production department needs to purchase a new machine. As the machine ages, it requires additional maintenance and also has a higher defect rate. The production department plans to replace the machine every few years. The purchase price of a new machine is $10,000. The maintenance cost and cost of defective product is given below. A used machine has no resale value. Age of machine Maintenance Cost Cost of Defects First Year $3,000 $2,000 Second Year $4,000 $4,000 Third Year $6,000 $7,000 Fourth Year $10,000 $11,000 a) Formulate a linear programming model to determine the best replacement policy over the next four years. What is the best replacement policy over the next four years? 2. A production department needs to purchase a new machine. As the machine ages, it requires additional maintenance and also has a higher defect rate. The production department plans to replace the machine every few years. The purchase price of a new machine is $10,000. The maintenance cost and cost of defective product is given below. A used machine has no resale value. Age of machine Maintenance Cost Cost of Defects First Year $3,000 $2,000 Second Year $4,000 $4,000 Third Year $6,000 $7,000 Fourth Year $10,000 $11,000 a) Formulate a linear programming model to determine the best replacement policy over the next four years. What is the best replacement policy over the next four years