1. Sensitivity Analysis Yet Another Furniture Factory (YAFF) have emplyed a researcher to analyse their production of Bookcases, Chairs and Desks. Management wish to maximise their daily profit, earned at the rate of $19 per bookcase, $12 per chair, and $17 per desk, but they are concerned that their production is limited by the availability of labour (225 hours per day) metal (117 units per day) and wood (420 units per day). The researcher has formulated a table of the constraints: obj bookcase(r, ) chair(12) desk(ry) 81 82 $3 right side Resource 19 -12 17 0 0 0 labour O 1 0 0 225 metal 1 0 117 wood 0 120 Subsequently the following final tableau was found: 0 0 0 1 3 1827 1 0 2 -1 39 48 30 (a) From the given final tableau, what are the dual prices of the resources? Explain why the dual prices show that the tableau presents an optimal primal solution. Is this the only optimal solution? Answer each of the following exercises independently of the others. Refer to the results in the above tableau for the original YAFF problem, and solve each of the variations 'by hand', showing all your working. Of course you may use software (Excel?) to check your answers. (b) Suppose that the availability of metal changes to 117 + Ab2. Use B-1 from the final tableau to find the solution corresponding to basis {71, 12, 23} in terms of Ab2. For what range of values of Ab, is this solution feasible (and therefore optimal)? What is the optimal solution if the availability of metal is reduced to 110 units per day? (c) Changing the profit margin per bookcase would mean replacing c1 = 19 by 19 + Ac. Do the algebra necessary to determine how much the profit per bookcase can increase or decrease without changing the optimal solution. If the profit per bookcase becomes $23 (Aci = 4), which variable would be a candidate to enter the basis, and which variable would be leaving