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# hw1_sol - SolutionforHW#1 Solution for HW#1 of Operations...

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OR methods for Profit and Value Engineering Solution for HW#1 1 / 6 Solution for HW#1 of 1. P21 Problem 12 Solution: Operations Research Methods for Profit and Value Engineering The following table provides the basic data of the problem (Suppose time to produce a Type 2 hat is T): Required Labor Time Profit(\$) Market limit Type 1 Hat 2T 8 150 Type 2 Hat T 5 200 Labor time limit 400T For the Wild West problem we need to determine the daily amounts to be produced of Type 1 and Type 2 hats. Thus the variables of the model are defined as x 1 = hats produced daily of Type 1 x 2 = hats produced daily of Type 2 Since Wild West want to maximize the total daily profit. It follows that Profit from Type 1 hat= 8 x 1 Profit from Type 2 hat=5 x 2 Letting z represent the total daily profit, the objective of Wild West is Maximize z =8 x 1 +5 x 2 The constraints restrict labor time and market limit are expressed as: ! 1 " 150 ! 2 " 200 2 # \$ ! 1 + # \$ ! 2 " 400T that is 2 ! 1 + ! 2 " 400 Thus, the complete Wild West model is Maximize z =8 x 1 +5 x 2 Subject to ! 1 " 150 ! 2 " 200 2 ! 1 + ! 2 " 400 ! 1 , ! 2 % 0 The solution of the LP problem is: ! 1 = 100; ! 2 = 200; then & = 1800 2. P21 Problem 15 Solution: The following table provides the basic data of the problem: Cost Reached audiences Allocated limit of total budget First ad Additional ad Radio \$300 5,000 2,000 80% TV ad \$2,000 4,500 3,000 80% Budget limit \$20,000 For the Top Toy problem we need to determine the amount of budget allocated to radio

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OR methods for Profit and Value Engineering Solution for HW#1 2 / 6 commercial and TV ad separately. Thus the variables of the model are defined as x 1 = number of radio commercial x 2 = number of TV ad P.S.: both x 1 and x 2 should be integers Since Top Toy want to maximize the total people could be reached by radio commercial and TV ad. It follows that People reached by radio commercial= 5,000+2,000 ×( x 1 ! 1) People reached by TV ad=4,500+3,000 ×( x 2 ! 1) Letting z represent the total people can be reached, the objective of Top Toy is Maximize z =[5,000+2,000 ×( x 1 ! 1)] " [ 4,500+3,000 ×( x 2 ! 1)] that is, Maximize z =4,5000+2,000 x 1 " 3,000 x 2
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hw1_sol - SolutionforHW#1 Solution for HW#1 of Operations...

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