Problem 3-02 (Algorithmic) Consider the following linear program: Max 3A+2B s.t. 1A+1BEB 3A+1B521 1A+2B514 $320 The value of the optimal solution is 22.5. Suppose that the righthand side of the constraint 1 is increased from B to 9. ) a. Use the graphical solution procedure to nd the new optimal solution. B B (i) 26+ \"\" 26+ 24 24 22 20 22 20 _ _ Optimal Solution 0p_nmal s_olmmn A = 56, B = 4,2 A6,B3 3A+2B=25_2 3A+2B=24 8101214161520 8101214161820 (iii) 3 (iv) 3 Solution A=0,B=9 3A+ZB=18 OptinalSolInion A=9,B=0 3A+2B=2? 81012141613 20 2468101214161520 lGraEE m vi J b. Use the solution to part(a) to determine the dual value for constraint 1. If required, round your answer to 1 decimal place. Dual Value: X c. The computer solution for the linear program in Problem 1 provides the following righthandside range information: RHS Allowable Allowable Constraint Value Increase Decrease 1 8.00000 1.80000 1.00000 2 21.00000 3.00000 9.00000 3 14.00000 Innite 4.50000 What does the righthandside range information for constraint 1 tell you about the dual value for constraint 1? If required, round your answers to ve decimal places. The right hand side range for constraint 1 isSt 0:. As long as the right- hand side stays within this range the dual valueIIs app Ica e v: d. The dual value for constraint 2 is 0.5. Using this dual value and the righthandside range information in part (c), what conclusion can be drawn about the effect of changes to the righthand side of constraint 2? If required, round your answers to 1 decimal place. The improvement in the value of the optimal solution will be S for every unit increase in the rightihand side of constraint 2 as long as the righthand side is between S ands . Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $65, $97, and $139, respectively. The production requirements per unit are as follows: Number of Number of Manufacturing Fans Cooling Coils Time (hours) Economy 8 Standard 12 AN Deluxe 14 For the coming production period, the company has 350 fan motors, 360 cooling coils, and 3000 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: Max 65E + 975 + 139D s.t. 16 + 15 + 1D $ 350 Fan motors 16 + 25 + 4D 360 Cooling coils BE + 125 + 140