Quantitative Techniques– 1b Q.1. Firm manufactures 3 products tables, chairs and stools. The resource requirements, availability and profit per unit of these products is given in the table below:...

Quantitative Techniques– 1b Q.1. Firm manufactures 3 products tables, chairs and stools. The resource requirements, availability and profit per unit of these products is given in the table below: PRODUCT RESOURCE Timber (Cubic feet) Production (hours) Polishing (hours) Profit Per Unit Rupees Table 10 7 2 12 Chair 2 3 4 3 Stool 1 2 1 1 Availability 100 77 80 - This has been solved as an LPP and the optimal solution is given below where S1, S2, S3 stand for the various slacks in timber, production and polishing departments respectively. 12 3 1 0 0 0 Contribution Basis X1 X2 X3 S1 S2 S3 RHS 12 X1 1 0 -1/16 3/16 -1/8 0 73/8 3 X2 0 1 13/6 -7/16 5/8 0 35/8 0 X3 0 0 -17/8 11/8 -9/4 1 177/4 You are required to carry out the sensitivity analysis in respect of the following issues parameter. Within what range of timber availability and production time will the basic remain unchanged? Write the solution values of the dual variables from the optimal table above Carry out a contribution ranging from basic and non-basic variables By incurring additional cost it would be possible to get additional timber. What should you be willing to pay for it? Should the feasibility of a new product teapoy be examined if it has a profit of Rs 4 and consume 3 units of each resource. Will it be possible to make stools profitable by reducing their timber consumption to 0 and using square plywood pieces which are available for free? Q.2 . A housewife buys 3 kinds of detergents D1, D2, D3. She never buys the same detergent in successive weeks. If she buys D1, then the next week she buys D2. However if she buys D2 or D3 then the next week she is 4 times likely to buy D1 as the other brand. Obtain the probability matrix for various transitions as brought out and the long term chances of various detergents being bought. Q.3. The stock market is presently experiencing a boom period which appears to have stretched for a long...