LG owns five production plants where 90″ high definition televisions are produced. LG can sell up to 25,000 televisions per year at the price of $4000 per television. For each plant, the production capacity, the production cost per television, and the fixed cost of operating a plant for year are given below. Production Plant Cost per Plant Capacity Fixed Cost Television 1 10000 $9 million $1,600 2 8000 $5 million $2,000 3 9000 $3 million $2,300 4 7000 $4 million $2,100 5 6000 $1 million $2,400 a. Use Solver to determine how LG can maximize its yearly profit from television production. b. Use SolverTable to determine how the optimal plant locations vary as the number of televisions that can be sold varies from 20,000 to 30,000 (in 1000 unit increments).

Plant Production Capacity Fixed cost Variable cost per TV Let
1 10000 $9,000,000.00 $1600 X1 Number of TV manufactured in Plant 1
2 8000 $5,000,000.00 $2000 X2 Number of TV manufactured in Plant 2
3 9000 $3,000,000.00 $2300 X3 Number of TV manufactured in Plant 3
4 7000 $4,000,000.00 $2100 X4 Number of TV manufactured in Plant 4
5 6000 $1,000,000.00 $2400 X5 Number of TV manufactured in Plant 5
Y1 Binary Variable (1 if X1>0 else 0)
Y2 Binary Variable (1 if X2>0 else 0)
Y3 Binary Variable (1 if X3>0 else 0)
Y4 Binary Variable (1 if X4>0 else 0)
Y5 Binary Variable (1 if X5>0 else 0)
Objective Function
Profit= Number of TVs from each plant* Selling Price-Fixed Cost-Number of TVs from Each Plant * Variable cost in that plant location
Profit= (X1+X2+X3+X4+X5)*4000 -( 9,000,000Y1+5,000,000Y2-3,000,000Y3-4,000,000Y4-1,000,000Y5)-(X1*1600-X2*2000-X3*2300-X4*2100-X5*2400)
Profit= 4000X1+4000X2+4000X3+4000X4+4000X5-1600X1-2000X2-2300X3-2100X4-2400X5-(9,000,000Y1+5,000,000Y2-3,000,000Y3-4,000,000Y4-1,000,000Y5)
Z= 2400X1+2000X2+1700X3+1900X4+1600X5-(9,000,000Y1+5,000,000Y2-3,000,000Y3-4,000,000Y4-1,000,000Y5)
Subject to
Constraint 1
Maximum Sales can be 25000
X1+X2+X3+X4+X5=0
Binary Variables
Y1,Y2,Y3,Y4,Y5 are binary variables
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b)
Selling Capacity
X1 X2 X3 X4 X5
20000 0 8000 9000 0 3000
21000 0 8000 9000 0 4000
22000 9000 0 0 7000 6000
23000 10000 0 0 7000 6000
24000 10000 8000 0 0 6000
25000 10000 0 9000 0 6000
26000 9000 8000 9000 0 0
27000 10000 8000 9000 0 0
28000 10000 0 0 7000 6000
29000 0 8000 9000 6000 6000
30000 9000 8000 0 7000 6000
 
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