1- SENSATIVITY ANALYSIS / LINEAR PROGRAMMING MODELS
Two models of colour 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 labour 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 can’t sell more than 12 sets of Alpha. Each unit of the Alpha model needs two hours of labour and 1 hour of machine time. The Beta model needs 1 hour of labour 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 supposed that management had a single goal of maximizing profit. Now suppose that the firm is moving to a new location at the time of a particular production period and feels that maximizing profit is not a realistic goal. Management sets a profit level that will 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 need to produce at least seven ceiling fans.
Formulate and solve the GOAL PROGRAMMING Problem for parts 1 and 2