Please just find the constraints and the linear problem that will maximize Jackson's profit.

Jackson Manufacturing produces generic Apple IPODs. They have plants in four locations and they distribute to four stores that will sell their merchandise for them. The four plants can produce up to 1000 , 3500 , and 5000 , and 8000 IPODS, respectively during the next month. Jackson Manufacturing has an order for exactly 4000 units for store 1 . Store 2 is requesting between 2000 to 4000 units. Store 3 is requesting no more than 3,000 units. Store 4 is requesting exactly 2000 units. The unit profit per IPOD sold is given in the following table. Additionally, there is a fixed cost to run each plant (and Jackson Manufacturing can decide which plants to run for the month). The fixed cost for each for the four plants is as follows: Plant 1, \$150000, Plant 2, \$140000, Plant 3, \$170000, Plant 4, \$120000. Managerial Report Analyze the manufacturing problem at Jackson Manufacturing, and prepare a report presenting your findings and recommendations. Include (but do not limit your discussion to) a consideration of the following items: a) Create and solve a linear problem that can be used to maximize Jackson Manufacturing's profit. List out how many IPODS to send from each plant to each store. b) What is the maximum profit? c) Suppose store 4 will take as many IPODS that are produced. However, after 2000 units, they would like a discount on the price of \$10 (yielding \$10 less on all of the revenues below). What is the new optimal solution d) What is the new maximum profit? e) Continuing with the conditions set in part c, if the fixed costs increased by 50% for each plant, what would the optimal solution be? List out how many IPODS to send from each plant to each store. What is the new maximum profit? f) Continuing with the conditions set in part c, if the fixed costs doubled for each plant, what would the optimal solution be? List out how many IPODS to send from each plant to each store. What is the new maximum profit? Note: For parts c, e and f, be sure to define any additional variables and list any extra constraints that need to be used in your discussion. Jackson Manufacturing produces generic Apple IPODs. They have plants in four locations and they distribute to four stores that will sell their merchandise for them. The four plants can produce up to 1000 , 3500 , and 5000 , and 8000 IPODS, respectively during the next month. Jackson Manufacturing has an order for exactly 4000 units for store 1 . Store 2 is requesting between 2000 to 4000 units. Store 3 is requesting no more than 3,000 units. Store 4 is requesting exactly 2000 units. The unit profit per IPOD sold is given in the following table. Additionally, there is a fixed cost to run each plant (and Jackson Manufacturing can decide which plants to run for the month). The fixed cost for each for the four plants is as follows: Plant 1, \$150000, Plant 2, \$140000, Plant 3, \$170000, Plant 4, \$120000. Managerial Report Analyze the manufacturing problem at Jackson Manufacturing, and prepare a report presenting your findings and recommendations. Include (but do not limit your discussion to) a consideration of the following items: a) Create and solve a linear problem that can be used to maximize Jackson Manufacturing's profit. List out how many IPODS to send from each plant to each store. b) What is the maximum profit? c) Suppose store 4 will take as many IPODS that are produced. However, after 2000 units, they would like a discount on the price of \$10 (yielding \$10 less on all of the revenues below). What is the new optimal solution d) What is the new maximum profit? e) Continuing with the conditions set in part c, if the fixed costs increased by 50% for each plant, what would the optimal solution be? List out how many IPODS to send from each plant to each store. What is the new maximum profit? f) Continuing with the conditions set in part c, if the fixed costs doubled for each plant, what would the optimal solution be? List out how many IPODS to send from each plant to each store. What is the new maximum profit? Note: For parts c, e and f, be sure to define any additional variables and list any extra constraints that need to be used in your discussion