APPROACH Formulate this production-mix situation as an LP problem. The production manager first specifies production levels for each product for the coming month. He lets: Xị = number of units of XJ201 produced X; = number of units of XM897 produced X3 = number of units of TR29 produced X4 = number of units of BR788 produced SOLUTION The LP formulation is: Objective: Maximize profit = 9X1 + 12X, + 15X3 + 11X4 subject to: 5x, + 1.5X2 + 1.5Xz + 1X4 < 1,500 hours of wiring available 3X, + 1X, + 2X3 + 3X s 2,350 hours of drilling available 2X, + 4X2 + 1X3 + 2X4 s 2,600 hours of assembly available .5X, + 1X, + 5X + .5X4 s 1,200 hours of inspection X1 2 150 units of XJ201 X, 2 100 units of XM897 X3 2 200 units of TR29 X4 2 400 units of BR788 X1, X2, X3, Xg 2 0
APPROACH Formulate this production-mix situation as an LP problem. The production manager first specifies production levels for each product for the coming month. He lets: Xị = number of units of XJ201 produced X; = number of units of XM897 produced X3 = number of units of TR29 produced X4 = number of units of BR788 produced SOLUTION The LP formulation is: Objective: Maximize profit = 9X1 + 12X, + 15X3 + 11X4 subject to: 5x, + 1.5X2 + 1.5Xz + 1X4 < 1,500 hours of wiring available 3X, + 1X, + 2X3 + 3X s 2,350 hours of drilling available 2X, + 4X2 + 1X3 + 2X4 s 2,600 hours of assembly available .5X, + 1X, + 5X + .5X4 s 1,200 hours of inspection X1 2 150 units of XJ201 X, 2 100 units of XM897 X3 2 200 units of TR29 X4 2 400 units of BR788 X1, X2, X3, Xg 2 0
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Solve this LP problem as formulated. What is the solution?
(NOTE: see attached images for the problem and its infos. Please answer it with solutions. Thank you so much!! Godbless!)
![INSIGHT There can be numerous constraints in an LP problem. The constraint right-hand sides may
be in different units, but the objective function uses one common unit-dollars of profit, in this case.
Because there are more than two decision variables, this problem is not solved graphically.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c28d09b-638e-4774-8058-2300f3240464%2F6314c4cf-5779-404a-8cbe-697da39ee747%2Fqp5kf9p_processed.png&w=3840&q=75)
Transcribed Image Text:INSIGHT There can be numerous constraints in an LP problem. The constraint right-hand sides may
be in different units, but the objective function uses one common unit-dollars of profit, in this case.
Because there are more than two decision variables, this problem is not solved graphically.
![APPROACH Formulate this production-mix situation as an LP problem. The production manager
first specifies production levels for each product for the coming month. He lets:
X = number of units of XJ201 produced
X2 = number of units of XM897 produced
X3 = number of units of TR29 produced
X4 = number of units of BR788 produced
SOLUTION The LP formulation is:
Objective: Maximize profit = 9X1 + 12X2 + 15X3 + 11X4
subject to:
.5X, + 1.5X2 + 1.5X3 + 1X4 s 1,500 hours of wiring available
3X1 + 1X2 + 2X, + 3X4 s 2,350 hours of drilling available
+ 2X4 s 2,600 hours of assembly available
2X1 + 4X2 + 1X3
.5X1 + 1X2 + 5X3 + .5X4 s 1,200 hours of inspection
X1 2 150 units of XJ201
X2 2 100 units of XM897
X3 2 200 units of TR29
X4 2 400 units of BR788
X1, X3, X3, X4 2 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c28d09b-638e-4774-8058-2300f3240464%2F6314c4cf-5779-404a-8cbe-697da39ee747%2Fjduthd_processed.png&w=3840&q=75)
Transcribed Image Text:APPROACH Formulate this production-mix situation as an LP problem. The production manager
first specifies production levels for each product for the coming month. He lets:
X = number of units of XJ201 produced
X2 = number of units of XM897 produced
X3 = number of units of TR29 produced
X4 = number of units of BR788 produced
SOLUTION The LP formulation is:
Objective: Maximize profit = 9X1 + 12X2 + 15X3 + 11X4
subject to:
.5X, + 1.5X2 + 1.5X3 + 1X4 s 1,500 hours of wiring available
3X1 + 1X2 + 2X, + 3X4 s 2,350 hours of drilling available
+ 2X4 s 2,600 hours of assembly available
2X1 + 4X2 + 1X3
.5X1 + 1X2 + 5X3 + .5X4 s 1,200 hours of inspection
X1 2 150 units of XJ201
X2 2 100 units of XM897
X3 2 200 units of TR29
X4 2 400 units of BR788
X1, X3, X3, X4 2 0
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