Two models of color TV sets designated Alpha and Beta are produced by Allison Company. The profit on Alpha is $300 and the profit on Beta is $250. There are 40 hours of labor each day in the production department and 45 hours of machine time available each day. The company can sell as many sets of model Beta as it can make, but it cannot sell more than 12 sets of Alpha. Each unit of the Alpha model requires two hours of labor and 1 hour of machine time. The Beta model requires 1 hour of labor and three hours of machine time.
FORMULATE AN LINEAR PROGRAM MODEL AND SOLVE THE PROBLEM.
Include the 4 steps of:
1. Defining the variables
2. State the objective function
3. State the content constraints
4. State the non negative constraints
Also, use
1. slack variables,
2. create a tableau and
3. include range of optimality
2 - GOAL PROGRAMMING / LINEAR PROGRAMMING MODELS
Part 1
Harrison Electric Company produces two products popular with home renovators: old-fashion chandeliers and ceiling fans. Both the chandeliers and fans require a two-step production process involving wiring and assembly. It takes about 2 hours to wire each chandelier, and 3 hours to wire a ceiling fan. Final assembly of the chandeliers and fans requires 6 and 5 hours respectively. The production capability is such that only 12 hours of wiring time and 30 hours of assembly time are available each day. If each chandelier nets the firm $7 and each fan $6, formulate a production mix decision LP.
Part 2
In the above portion of this problem, you assumed that management had a single goal of maximizing profit. Now assume that the firm is moving to a new location during a particular production period and feels that maximizing profit is not a realistic goal. Management sets a profit level, which would be satisfactory during the adjustment period, of $30. Harrison has established the following goals in order of priority (i.e., the first one listed is the most important): Formulate a GP Model.
1. To produce as much profit above $30 as possible during the production period.
2. To fully utilize the available wiring department hours.
3. To avoid overtime in the assembly department.
4. To meet a contract requirement to produce at least seven ceiling fans.