(1). A company produces items at three plants. At each plant, the labor, raw material and production costs (excluding labor cost) required to build an item are: plant labor (hours) required raw material required production cost 1 2 3 20 16 10 5 8 7 50 80 100 Each plant has sufficient machine capacity to produce up to 750 items per week. Each of the company's workers can work upto 40 hours per week and is paid $12.50 per hour worked. The company has 525 workers and 9400 units of raw material. Each week at least 1400 items must be produced. Define x; number of items produced at plant i = 1,2,3 each week. The Lindo output to minimize the company's total cost (labor and production) is given below: (a). What would be the new optimal solution if the production cost at plant 1 was only $ 40? (b). Find the new optimal solution if the capacity at plant 3 is increased by 100 items? (c). What would be the company's cost if it had to produce 100 more items? (d). What would be the new optimal solution if the production cost at plant 1 was only $40 and the capacity at plant 3 is increased by 100 items?