4 products: VCR, Stereo, TV, DVD
3 resources: electric component, nonelectric component, time
VCR
Stereo
TV
DVD
supply
ele. comp
($7/unit)
3
4
4
3
4700
nonele. comp
($5/unit)
2
2
4
3
4500
time
($10/unit)
1
1
3
2
2500
$70
$80
$150
$110
unit selling price
1. Write a LP model.
2. Use the Solver to solve the problem.
3. Based on the sensitivity report, answer the following questions:
(1) What if the supply of nonelectrical components changes?
Shadow price of nonele comp. is 0, 4500 changes in (4500-560,infinity), total profit
unchanged
(2) What happens if the supply of electrical components

increased by 400 (to 5100)? 在增量的范围之内，400*2=$800,
profit=69400+800=70200

increased by 4000 (to 8700)? Uncertain , 超过了增量范围
(3) What if we could buy an additional 400 elec. components for $1 more than usual?
Would we want to buy them?
Yes, total profit increase$2, total cost increase $1
Total profit will increase $2-$1
If we buy 400 additional elec.comp, total profit will increase 400*$1=$400
(4) What if we could get an additional 250 hours of assembly time by paying $5 per
hour more than usual? Would this be profitable?
24+5=29
29*250=7250
(5) What happens if we make VCR?
Reduced cost of VCR= unit profit- worth of resources used by VCR =
29-(3*$2+2*0+1*$24)=-1
If we produce one VCR, total profit decreases $1
(6) What should we do before we would want to begin making VCR’s?
To make VCR, the unit profit of VCR=$30, selling price of VCR increases to $71
(7) For what range of DVD prices will the current solution remain optimal?
Unit profit of DVD is $54, if it ranges (54-5, 54+10), current optimal solution
unchanged. DVD price can be changed in (110-5, 110+10), optimal solution
unchanged.
(8) What happens to profit if DVD selling price drops to $106?
DVD price decreases by $4, unit profit of $54 decreases by $4 in allowance decrease,
optimal solution unchanged
So, total profit decreases by $4*1060=$4240