Scenario 3: The ABC Corporation manufactures three electrical products; humidifi
ID: 3208186 • Letter: S
Question
Scenario 3: The ABC Corporation manufactures three electrical products; humidifiers, fans and air cleaners. The manufacturing process is composed of three processes: wiring, packaging and assembly. During the next production period, 2000 hours of wiring time are available, 60 hours of packing and up to 1500 hours of assembly time may be used. The following table presents the production requirements per unit: (5 points each for a total of 10 points)
Bill of Labor
Product
Wiring
Assembly
Packaging
Humidifiers
2 hrs.
3 hrs.
1.25 hrs.
Air Cleaners
1 hrs.
4 hrs.
0.75 hrs.
Fans
1.25 hrs.
2.1 hrs.
1.50 hrs.
Standard Costs
Product
Material
Labor
Overhead
Selling Price
Humidifiers
$17.50
$7.50
$26.45
$75
Air Cleaners
$26.15
$6.35
$19.75
$70
Fans
$6.55
$4.75
$9.55
$36.25
Formulate and solve this LP production mix situation to find the best combination of air conditioners, humidifiers and fans and that yields the highest profit. Feel free to use the Excel template provided or the corner point method.
: Round your Solution Values to a whole number and calculate the profit using the rounded solution.
Product
Wiring
Assembly
Packaging
Humidifiers
2 hrs.
3 hrs.
1.25 hrs.
Air Cleaners
1 hrs.
4 hrs.
0.75 hrs.
Fans
1.25 hrs.
2.1 hrs.
1.50 hrs.
Explanation / Answer
Let x be the number of Humidifiers,Y be the number of Air Cleaners, z be the number of Fans
Given2x+y+1.25z<=2000
3x+4y+2.1z<=1500
1.25x+0.75y+1.5z<=60
Profit=x(75-51.45)+y(70-52.25)+z(36.25-20.85)=23.55x+17.75y+15.4z
We need to maximize Profit
Hence Using a Solver, we get x=0,y=80,z=0, Maximum Profit=1420
This is due to lower time of Packagind in Air Cleaner.
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