Answer part (e) and (f)

That is all the information the problem gives.

2) A factory manufactures three products. Three resources-technical services, labor, and administration-are required to produce these products. The following table gives the requirements on each resource for the three products: Product Resources Labor Technical Services Administration Unit profits (5) 10 10 There are 100 hours of technical services available. 600 hours of labor, and 300 hours of administration. In order to determine the optimal product mix which will maximize the total profit the following linear program was solved. MAX Z=10X-+6X:+4X3 ST. Xr+ X2+ X: s100 10X1+4x2+5X3 5600 2X1+2X2+6X3 $300 where X1, X and Xare the number of product 1, product 2 and product 3 produced. The optimal solution is given by the following tableau. -16/6 -16/6 5/8 - 20/6 10/6 4400/ 6 0 0 400/6 0 1 200/6 1 0 10000 -1/8 1/6 -4/6 SOME RANGES IN WHICH THE BASIS IS UNCHANGED OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE 10.0000 5.0000 4.0000 6.0000 4.0000 2.0000 RIGHTHAND SIDE RANGES RESTRICTION CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 600.0000 399.9999 199.9985 300.0000 INFINITY 100.0000 Using sensitivity analysis, answer the following with respect to the above tableau. a) What should be the profit of product 3 before it becomes worthwhile to manufacture? b) If the profit of product 1 increases to 12. what would be the new optimal solution? C) What is the range on the profit of product 1 so that the current solution is still optimal? d) Which restriction would you increase and why? e) It is believed that the estimates of the available hour of technical services might be wrong. The correct estimate us 100 + 10% where is some unknown parameter. Find the range of values of 2 within which the given product mix is still optimal. 1) The manufacturing department comes up with a proposal to produce a new product requiring 1 hour of technical service, 4 hours of labor, and 3 hours of administration. The marketing and sales department predicts that the product can be sold at a unit profit of $8. What should be the management's decision