Reference no: EM133039477
Racer Maker produces and sells toy racing cars that resemble machines used in Formula One races. The new GM of Racer Maker has asked you as the Production Manager to plan production for the last three months for the year. He has also emphasized the need for minimization of the production costs involved.
The Marketing Manager gave you the demand forecasts for 3 popular toy racing cars sold by Racer Maker, viz: Ferrari, Maserati and Williams. They are presented in the table below:
|
Month
|
Ferrari
|
Maserati
|
Williams
|
|
October
|
740
|
750
|
700
|
|
November
|
780
|
800
|
720
|
|
December
|
950
|
900
|
800
|
Your production supervisor also gave you the following key information regarding the required production resources for this planning period. These are presented in Table 2 below:
|
Month
|
Machine Time available (hours)
|
Available Labour Hours
|
|
October
|
3500
|
3000
|
|
November
|
3700
|
3500
|
|
December
|
4000
|
4200
|
Other key information gathered by your production supervisor include the following to assist you in optimising the cost of production. These are presented in the following tables:
|
Car Model
|
Machine Time per unit (hours)
|
Labour Hours oer unit of toy car (hours)
|
|
Ferrari
|
1.2
|
1.1
|
|
Maserati
|
1.3
|
1.2
|
|
Williams
|
1.5
|
1.25
|
|
Model
|
Production Cost per toy car
|
|
Ferrari
|
$15
|
|
Maserati
|
$18
|
|
Williams
|
$13
|
You intend to use Linear Programming to determine the minimum cost of production.
Your GM later expressed confidence at securing a cheaper source of raw materials for the production of Ferrari and Maserati toy cars for the period of October. He would like you to consider lowering the unit cost of production for the Ferrari and Maserati toy cars for October by $2 each. He requested you to provide him with information on the improvement in the optimal production cost.
Based on the given information:
(a) Develop a linear programming (LP) model to minimise the production costs of Racer Maker for the planning period of October to December. Your model must be in the form of algebraic equations and inequalities where appropriate. State your assumptions in constructing your LP model (Note: Your assumptions must be specific to the LP problem)
(b) Solve the LP model using the Excel Solver and present your Answer and Sensitivity Reports. Interpret the terms "Binding" and "Not-binding" indicated in your Answer Report by referring to the appropriate decision variables.
(c) Without using the Excel Solver, determine the lower cost of production from purchasing the raw materials from a cheaper source for the October production and inform the GM the cost improvement accordingly.