The LP problem whose output follows determines how many necklaces, bracelets, rings, and earrings a jewelry store should stock (measured in stocking units). The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space capacity in units, constraint 2 measures time to set up the display in minutes. Constraints 3 and 4 are marketing restrictions.
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MAX
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100X1+120X2+150X3+125X4
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1) X1+2X2+2X3+2X4
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2) 3X1+5X2+X4
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3) X1+X3
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4) X2+X3+X4>50 plus nonnegativity
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Target Cell (Max)
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Cell
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Name
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Final Value
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$B$9
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profit
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7475
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Adjustable Cells
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Final
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Reduced
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Objective
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Allowable
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Allowable
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Cell
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Name
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Value
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Cost
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Coefficient
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Increase
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Decrease
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$G$3
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x1 (necklaces)
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8
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0
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100
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1E+30
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12.5
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$G$4
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x2 (bracelets)
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0
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-5
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120
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5
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1E+30
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$G$5
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x3 (rings)
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17
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0
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150
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12.5
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25
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$G$6
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x4 (earrings)
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33
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0
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125
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25
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5
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Constraints
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Final
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Shadow
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Constraint
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Allowable
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Allowable
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Cell
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Name
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Value
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Price
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R.H. Side
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Increase
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Decrease
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$C$7
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usage space
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108
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75
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108
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15.75
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8
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$D$7
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usage setup time
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57
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0
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120
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1E+30
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63
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$E$7
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usage marketing1
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25
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25
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25
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33
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17
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$F$7
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usage marketing2
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50
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-25
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50
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4
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8.5
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Use the output to answer the questions:
What is the optimal solution and what profit will it return?
How much would you be willing to pay to reduce the setup time restriction by 20 minutes?
If the profit for 1 unit of necklace were to drop by $10 what impact will this have?
Do the same for earrings?
What if the profit for necklaces and the profit for rings were both to drop by $5? What could we say then?
The jewelry store is considering having watches as well. Watches take up 3 units of space and one unit of set up time. They also contribute one unit to each of the marketing restrictions (rhs decreases by 1 for each). How much profit would be needed to make it worthwhile to store watches?
You are offered the chance to obtain more space. The offer is for 15 units and the total price is 1000. What should you do? How about 16 units for the same price?
How would the solution change if the profit for bracelets was to increase to 122/unit? What about profit?