Question: The Manning Metal Milling Company Problem. The J.J. Manning Metal Milling Company makes three products, flywheels, u-joints and axles. The manager is faced with the problem of deciding the best output schedule for the upcoming month. Management and staff have arrived at a table of data for the upcoming month:

It has been determined that there at most 1,620 hours of production time available next month, at a unit cost of $7.00 per hour. There is no limit on the supply of metal for the production runs, however each unit of metal will cost $2.00.

The company is experiencing a severe cash flow problem. Consequently all sales are made for cash, and all fixed costs and variable must be paid for in cash during the month of production. Fixed costs for the month will be $2,200, and there will be a payment on a loan due for $800. The cash balance at the beginning of the month is $28,125, and Manning Metal Milling would want to leave no less that $5,000 in the till at the end of the month.

Develop management's production program by linear programming so as to maximize profits.

(Solution: Interesting problem. Produce no flywheels, 550 u-joints and only 175 axles. All the labor will be utilized. The profit will be $9,742. There is no problem with the cash flow. Operations will produce a positive cash balance of +$37,067.00)