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0x0 Y 3.6.2 3.6 Sensitivity Analysis 129 (b) If the revenue per ton of exterior paint remains constant at $3000 per ton, determine the maximum unit revenue of interior paint that will keep the present optimum salu- tion unchanged. (e) Ifíor marketing reasons the unit revenue of interior paint must be reduced to $3000, will the current optimum production mix change? +3. In Problem 2, Set 3.6a: (a) Determine the optimality range for the unit revenue ratio of the two types of hats that will keep the current optimum unchanged. (b) Using the information in (b), will the optimal solution change ¡f the revenue per unit is the same for both types? Algebraic Sensitivity Analysis—Changes in the Right-Hand Side In Section 3.6.1, we used the graphical solution to determine the dual prices (the unit worths of resources) and their feasibility ranges. This section extends thc analysis to the general LP model. A numeric example (the TOYCO model) will be used to facilitate the presemation. Example 3.6-2 (TOYCO Model) TOYCO assembies three types of toys—trains, trucks, and cars—using threc operations. The daily limits on the available times for the three Operations are 430, 460, and 420 minutes, respec- tively, and the revenues per unit of toy train, truck, and car are $3, $2,and $5, respectively. The as- sembly times per train at the three operations are 1, 3, and 1 minutes, respectively. The corresponding times per train and per car are (2,0, 4) and (1,2,0) minutes (a zero time indicates that the operation is not used). Letting x,, xz, and x3 represent the daily number of units assembled of trains, trucks, and cars, respectively, the associated LP model is given as: Maximize z = 3x, + 2x) + 5x3 subject to 21 + 2x7 + x3 <= 430 (Operation 1) 3x0 + 2x3 < 460 (Operation 2) Xi + 4x <= 420 (Operation 3) 11,5 >0 Using x<, x5, and xg as the slack variables for the constraints of operations 1,2, and 3, respective- 1y, the optimum tableau is KIáAK ——— > Basio 51 xa xx xa xs x6 Solution A z 4.0. 0. 1. 2.00 1350 IA x 4 01. 0 | 4 0 100 x 30 0. 1. 0 qo0 230 Xo 2 0. 2 1 20