Failsafe Electronics Corporation primarily manufactures four highly technical products, which it supplies to aerospace firms that hold NASA contracts. Each of the products must pass through the following depart- ments before they are shipped: wiring, drilling, assembly, and inspection. The time requirements in each department (in hours) for each unit produced and its corresponding profit value are summarized in this table: DEPARTMENT PRODUCT WIRING INSPECTION UNIT PROFIT DRILLING ASSEMBLY XJ201 .5 2 .5 $9 хм897 1.5 1 4 1.0 $12 TR29 1.5 1 .5 $15 BR788 1.0 3 2 .5 $11 The production time available in each department each month and the minimum monthly production requirement to fulfill contracts are as follows: DEPARTMENT CAPACITY (HOURS) PRODUCT MINIMUM PRODUCTION LEVEL Wiring 1,500 X1201 150 Drilling 2,350 XM897 100 Assembly 2,600 TR29 200 Inspection 1,200 BR788 400

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Failsafe Electronics Corporation primarily manufactures four highly technical products, which it supplies to aerospace firms that hold NASA contracts. Each of the products must pass through the following departments before they are shipped: wiring, drilling, assembly, and inspection. The time requirements in each department (in hours) for each product and its corresponding profit value are summarized below:

(see attached images for the complete details of the problem. Please answer it with solutions. Thank you so much! Godbless.)

Solve this LP problem as formulated. What is the solution?

A PRODUCTION-MIX PROBLEM
Failsafe Electronics Corporation primarily manufactures four highly technical products, which it supplies to
aerospace firms that hold NASA contracts. Each of the products must pass through the following depart-
ments before they are shipped: wiring, drilling, assembly, and inspection. The time requirements in each
department (in hours) for each unit produced and its corresponding profit value are summarized in this table:
DEPARTMENT
PRODUCT
WIRING
DRILLING
ASSEMBLY
INSPECTION
UNIT PROFIT
XJ201
.5
3
2
.5
$ 9
Xм897
1.5
4
1.0
$12
TR29
1.5
2
.5
$15
BR788
1.0
3
2
.5
$1
The production time available in each department each month and the minimum monthly production
requirement to fulfill contracts are as follows:
DEPARTMENT
CAPACITY (HOURS)
PRODUCT
MINIMUM PRODUCTION LEVEL
Wiring
1,500
XJ201
150
Drilling
2,350
ХM897
100
Assembly
2,600
TR29
200
Inspection
1,200
BR788
400
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:
X1 = 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 IR formulotion ig
Transcribed Image Text:A PRODUCTION-MIX PROBLEM Failsafe Electronics Corporation primarily manufactures four highly technical products, which it supplies to aerospace firms that hold NASA contracts. Each of the products must pass through the following depart- ments before they are shipped: wiring, drilling, assembly, and inspection. The time requirements in each department (in hours) for each unit produced and its corresponding profit value are summarized in this table: DEPARTMENT PRODUCT WIRING DRILLING ASSEMBLY INSPECTION UNIT PROFIT XJ201 .5 3 2 .5 $ 9 Xм897 1.5 4 1.0 $12 TR29 1.5 2 .5 $15 BR788 1.0 3 2 .5 $1 The production time available in each department each month and the minimum monthly production requirement to fulfill contracts are as follows: DEPARTMENT CAPACITY (HOURS) PRODUCT MINIMUM PRODUCTION LEVEL Wiring 1,500 XJ201 150 Drilling 2,350 ХM897 100 Assembly 2,600 TR29 200 Inspection 1,200 BR788 400 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: X1 = 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 IR formulotion ig
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 = 9X, + 12X3 + 15X3 + 11.X4
subject to:
5X, + 1.5X; + 1.5X, + 1X, s 1,500 hours of wiring available
3X, + 1X2 + 2X, + 3X4 s 2,350 hours of drilling available
2X, + 4X; + IX, + 2X, s 2,600 hours of assembly available
5X, + 1X + 5X3 + .5X4 s 1,200 hours of inspection
X = 150 units of XJ201
X = 100 units of XM897
X3 = 200 units of TR29
X4 2 400 units of BR788
X1, X3, Xy, Xg æ 0
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.
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 = 9X, + 12X3 + 15X3 + 11.X4 subject to: 5X, + 1.5X; + 1.5X, + 1X, s 1,500 hours of wiring available 3X, + 1X2 + 2X, + 3X4 s 2,350 hours of drilling available 2X, + 4X; + IX, + 2X, s 2,600 hours of assembly available 5X, + 1X + 5X3 + .5X4 s 1,200 hours of inspection X = 150 units of XJ201 X = 100 units of XM897 X3 = 200 units of TR29 X4 2 400 units of BR788 X1, X3, Xy, Xg æ 0 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.
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