A plant making cases of canned soup has total labor costs of:

Quantity range (speed)

Total labor cost

1-1000 cases/hr $100/hr

1001-2000 150

2001-3000 200

3001-4000 300

The plants utility cost if $50/hr regardless of the plant speed. Ingredients for the soup (including the cans and case boxes) cost $15.00/case. The factory can operate for 8 hours per day, 5 days per week.

1)Find the optimal speed at which to operate the soup factory (in cases/hr).

2)If the plant has a contract to deliver 100,000 cases of soup for a supermarket chain in one week, what speed should they operate at to minimize production costs and how many hours will it take?

3)What if the contract was for 150,000 cases?