Business Analysitcs 2nd Edition, Chapter 13 Problem 16 (linear optimization). I
ID: 372036 • Letter: B
Question
Business Analysitcs 2nd Edition, Chapter 13 Problem 16 (linear optimization). I am having trouble interpreting sensitivity report given in Excel. I would be grateful if someone could help me understand how to answer all parts of the question parts a through e. Thank you.
Figure shows the Solver sensitivity report for Valencia Products in Problem. Using only the information in the sensitivity report, answer the following questions a. Explain why the reduced cost for SpeedBuster is 0 b. If the unit profit for SpeedBuster is decreased to $35, can you predict how the optimal solution and profit wll change? c. If the unit profit for LaserStop is increased to $64, can you predict how the optimal solution and profit will change? d. If an additional 500 units of component A are available, can you predict how the optimal solution and profit will be affected? e. If a supplier delay results in only 3,400 units of component B available, can your predict how the optimal solution and profit will be affected? Figure Sensitivity Report for Valencia Products A B Final Value TOTAL PROFIT 0 Decsion Variable Cell ReducedObjective Allowable Allowable Cost Coefficlent Increase Decrease 12 Cell 13 | $8511 Numbers Produced LaserStop 0.00 333.33 36.00 0.00 24 36 E+30 15 16 Constraints 17 18 Cell 19 $0514 Component A Used Finel Shadow Constraint Allowable Allowable R.H. Side Increase Decrease Price 4000 3.333333333 4000 1500 1E+30 166.6666667 1s 8 Used Problem Valencia Products makes automobile radar detectors and assembles two models LaserStop and SpeedBuster. The firm can sell all it produces. Both models use the same electronic components. Two of these can be obtained only from a single supplier. For the next month, the supply of these is limited to 4,000 of component A and 3,500 of component B. The number of each component required for each product and the profit per unit are given in the table Components Required/Unit A B Profit/unit LaserStop 18 6 $24 SpeedBuster 12 10 $40Explanation / Answer
a) The reduced cost for Speedbuster is zero because:
reduced cost means that by the reduced cost figure the the cost should go down or profit should increase such that it becomes attractive to produce that item. Speedbuster is already the more attractive item hence its reduced cost is zero. This means reduction in profit will not result in higher sales of Speedbuster.
b) If the unit profit from Speedbuster were to be decreased to 35, it wont effect the optimal solution. Only the profit will go down by $5 per unit.
c) Laserstop reduced cost = 36. which means that the profit should increase by minimum $36 to make it more attractive. Hence, minimum the profit from Laserstop should be = 24+36 = $60. If we increase the profit to $64, the optimal solution will change and increase the production of Laserstop because it has become more attractive. If all production happens for Laserstop, the profit would be higher than current profit.
d) If additional 500 units of component A is available, upto 200 units the profit increase will be 3.3333 (shadow price) per unit increase in component A. After that Component B will become a constraint and rest 300 units of component A will not be used.
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