Explain and formulate a linear programming model

Linear Programming Model for Optimal Production schedule for Richard Manufacturing

Problem:

Richland Manufacturing Company manufactures solid oak computer desks on two separate production lines at its plant in Richland, Vermont. Production line 1 is continuously operated and is staffed with workers experienced in the construction of quality oak furnishings. Production line 2 is activated only when demand is high and/or when large orders cannot be met by the capacity of line 1 alone in a timely manner. Production line 2 is staffed by less-experienced, but equally paid, workers temporarily transferred from other production tasks, on a weekly basis, from within the company. Each production period at Richland consists of one week for scheduling purposes. Line 1 can produce 5 desks per hour, while only 3 desks per hour can be produced on line 2. The operational costs for each line are the same, and each line will have 40 hours of production time available for any production period. If line 2 is not needed, and therefore not scheduled, the production time available for that week is zero. The production manager has reviewed the current orders for computer desks and has established the following goals, in order of importance, for the next production period:

Produce at least 350 desks.
Limit overtime on line 1 to a maximum of 10 hours.
Operate both lines for a minimum of 40 hours each if line 2 is needed.

The production manager also insists that in attempting to meet company objectives, the first goal is five times more important than the second, and that the second goal is twice as important as the third.

a. Formulate a linear programming model that can be used to determine the optimal production schedule that will best achieve the goals of Richland Manufacturing Company.

b. Determine the optimal production schedule for Richland Manufacturing Company using the Management Scientist software, including the quantity of the product produced, the hours of production utilized, and the levels of goal achievement.

Then explain if acheivement or failure is indicated.