18. D Electronics produces three models of satellite dishes-Alpha, Beta and Gamma-which have contributions per unit of Rs 400, Rs 200 and Rs 100, respectively.

There is a two-stage production process and the number of hours per unit for each process are:

There is an upper limit on process hours of 1,920 per period for Process 1 and 2,200 for Process 2.
The Alpha dish was designed for a low-power satellite which is now fading and the sales manager thinks that sales will be no more than 200 per period. Fixed costs are Rs 40,000 per period.
You are required to

(a) formulate these data into a linear programming model using the following notation:
X2 number of alphas number of betas x3 number of gammas

(b) formulate (but do not attempt to solve) the initial Simplex Tableau using x4 as slack for Process 1 x5 as slack for Process 2 x6 as slack for any sales limit and describe the meaning of slack.

(c) interpret the final Simplex Tableau below:

Investigate the effect on the solution of each of the following:
(i) An increase of 20 hours per period in Process 1, (ii) An increase of 10 units per period in the output of Alpha,

(iii) Receiving an order, which must be met, for 10 units of Gamma.

Transcribed Image Text:

Process 1 Process 2 Alpha Beta Gamma 23 2 3 32 3 2.5 2 2