In a machine shop a company manufactures two types of electronic

components, X and Y on which it aims to maximize the contribution to profit.

The company wishes to know the ideal combination of X and Y to make. All the

electronic components are produced in three main stages: Assembly, Inspection and

testing, and packing. In Assembly each X takes 1 hour and each Y takes 2 hours.

Inspection & Testing takes 7.5 minutes for each X and 30 minutes for each Y on average,

which includes the time required for any faults to be rectified. In In total there are 600

hours available for assembly and 100 hours for inspection and testing each week. At all

stages both components can be processed at the same time. At the final stage the

components require carefully packing prior to delivery. Each X takes 3 minutes and each

Y take 20 minutes on average to mount, box and pack properly. There is a total of 60

packing hours available each week. The contribution on X is $10 per unit and on Y is $15

per unit. For engineering reasons not more than 500 of X can be made each week.

i. Formulate this problem as a linear programming problem by clearly defining

the decision variables, the objective function and the constraints.

ii. Use the graphical approach to advice the company on the optimum product

mix and contribution.

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