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ADM 3326 Lecture Notes - Lecture 8: Shadow Price

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purplesardine733
11 Jul 2016
School
University of Ottawa
Department
Administration
Course
ADM 3326
Professor
Raluca Balan

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Document Summary

X1= 4, x2 = 2 (intersection of constraint 2 with constraint 3) Problem #2: if it costs to produce 1000 tools at plant 1 and ship them to customer 1, what would be the new solution to the problem and the profit? ( 1 point) This corresponds to a decrease in the objective function coefficient of x11 from (= A decrease of is within the allowable decrease of 20 thus the optimal solution will not change however the profit will decrease. The optimal decision calls for the production of 10,000 tools at plant 1 and shipped to customer 1 (x11 = 10) and the production of 11,670 tools at plant 2 and shipped to customer 2 (x22 = 11. 67). The profit will decrease by and will be ,233. 33 (= 130(10) + 80(11. 67): if the price of an additional hour of labor were reduced to , would the company purchase any additional labor? (1 point)

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Related Questions

Need assistance with these problems!


1. The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X1 - X4 represent the number of employees starting work on each shift (shift 1 through shift 4).
Minimize X1 + X2 + X3 + X4
Subject to: X1 + X4%u2265 12 (shift 1)
X1 + X2%u2265 15 (shift 2)
X2 + X3%u2265 16 (shift 3)
X3 + X4%u2265 14 (shift 4)
all variables %u2265 0

Find the optimal solution using QM.
How many workers would be assigned to shift 1? (Points : 3) 12
13
0
none of the above

2. When appropriate, the optimal solution to a maximization linear programming problem can be found by graphing the feasible region and: (Points : 3)
finding the profit at every corner point of the feasible region to see which one gives the highest value.
moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is encountered.
locating the point that is highest on the graph.
none of the above.
all of the above.


3. Multiple optimal solutions can occur when the objective function is __________ a constraint line. (Points : 3)
unequal to
equal to
linear to
parallel to


4. When applying linear programming to diet problems, the objective function is usually designed to: (Points : 3)
maximize profits from blends of nutrients.
maximize ingredient blends.
minimize production losses.
maximize the number of products to be produced.
minimize the costs of nutrient blends.


5. For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the: (Points : 3)
same product mix, different total profit.
different product mix, same total profit as before.
same product mix, same total profit.
different product mix, different total profit.


6. The corner point solution method: (Points : 3)
will yield different results from the isoprofit line solution method.
requires that the profit from all corners of the feasible region be compared.
will provide one, and only one, optimum.
requires that all corners created by all constraints be compared.
will not provide a solution at an intersection or corner where a non-negativity constraint is involved.


7. Consider the following linear programming problem.
Maximize 4X + 10Y
Subject to: 3X + 4Y %u2264 480 and 4X + 2Y %u2264 3 360
all variables %u2265 0
The feasible corner points are (48,84), (0,120), (0,0), (90,0).

What is the maximum possible value for the objective function? (Points : 3)
1032
1200
360
none of the above


8. When using Excel's Solver to input and solve a linear programming problem, it is essential that one perform an additional task before submitting the formulation. That important additional function is: (Points : 3)
guessing the values of the variables.
putting in a value for the objective function.
choosing the options for assuming both a linear model and non-negative variables.
resetting the parameters.
none of the above.


9. Consider the following linear programming problem.
Maximize 5X + 6Y
Subject to: 4X + 2Y %u2264 420 and 1X + 2Y %u2264 120
all variables %u2265 0

Which of the following points (X,Y) is not feasible? (Points : 3)
(50,40)
(20,50)
(60,30)
none of the above


10. ____________ is used to analyze changes in model parameters. (Points : 3)
Optimal solution
Feasible solution
Sensitivity analysis
None of the above

Unter Components manufactures low-cost navigation systems forinstallation in ride-sharing cars. It sells these systems tovarious car services that can customize them for their locale andbusiness model. It manufactures two systems, the Star100 and theStar150, which differ in terms of capabilities. The followinginformation is available:

Costs per Unit Star100 Star150
Direct materials $ 70 $ 80
Direct labor 24 30
Variable overhead 10 15
Fixed overhead 95 125
Total cost per unit $ 199 $ 250
Price $ 280 $ 380
Units sold 4,000 2,000

The average wage rate is $15 per hour. Variable overhead varieswith the quantity of direct labor-hours. The plant has a capacityof 20,000 direct labor-hours, but current production uses only10,400 direct labor-hours.

Required:

a. A nationwide car-sharing service has offeredto buy 2,400 Star100 systems and 2,400 Star150 systems if the priceis lowered to $190 and $240, respectively, per unit.

a-1. If Unter accepts the offer, how manydirect labor-hours will be required to produce the additionalsystems?

a-2. Complete the following table to determinethe differential profit increase (or decrease) if Unter acceptsthis proposal. Prices on regular sales will remain the same. .

b-1. Supposed that the car-sharing service hasoffered instead to buy 3,400 each of the two models at $190 and$240, respectively. This customer will purchase the 3,400 units ofeach model only in an all-or-nothing deal. That is, Unter mustprovide all 3,400 units of each model or none. Unter's managementhas decided to fill the entire special order for both models. Inview of its capacity constraints, Unter will reduce sales toregular customers as needed to fill the special order. Complete thetable below to determine the total contribution margin with thespecial order added.

b-2. How much will the profits change if theorder is accepted? Assume that the company cannot increase itsproduction capacity to meet the extra demand.

c-1. Assume that, in the situation presented inrequirement b-1, the plant can work overtime. Direct labor costsfor the overtime production increase to $22.50 per hour. Variableoverhead costs for overtime production are $4 per hour more thanfor normal production. Complete the table below to determine thetotal contribution margin.

c-2. How much will the profits change in thissituation?

Hi-Speed Electronics manufactures low-cost, consumer-gradecomputers. It sells these computers to various electronicsretailers to market under store brand names. It manufactures twocomputers, the Lightning 2.0 and the Lightning 2.4, which differ interms of speed, included memory, and included hard drive capacity.The following information is available:

Costs per Unit Lightning 2.0 Lightning 2.4
Directmaterials $ 74 $ 84
Direct labor 32 40
Variableoverhead 15 20
Fixed overhead 99 129
Total cost perunit $ 220 $ 273
Price $ 290 $ 390
Units sold 4,000 2,000

The average wage rate is $20 per hour. Variable overhead varieswith the quantity of direct labor hours. The plant has a capacityof 20,000 direct labor-hours, but current production uses only10,400 direct labor-hours.

Required:
a.

A nationwide discount chain has offered to buy 2,500 Lightning2.0 computers and 2,500 Lightning 2.4 computers if the price islowered to $200 and $250, respectively, per unit.
a-1.

If Hi-Speed accepts the offer, how many direct labor-hours willbe required to produce the additional computers?
a-2.

How much will the profit increase (or decrease) if Hi-Speedaccepts this proposal? Prices on regular sales will remain thesame.
b.

Suppose that the nationwide discount chain has offered insteadto buy 3,500 each of the two models at $200 and $250, respectively.This customer will purchase the 3,500 units of each model only inan all-or-nothing deal. That is, Hi-Speed Electronics must provideall 3,500 units of each model or none. Hi-Speed's management hasdecided to fill the entire special order for both models. In viewof its capacity constraints, Hi-Speed will reduce sales to regularcustomers as needed to fill the special order. How much will theprofits change if the order is accepted? Assume that the companycannot increase its production capacity to meet the extrademand.
c.

Answer the question in requirement (b), assuming instead thatthe plant can work overtime. Direct labor costs for the overtimeproduction increase to $30.00 per hour. Variable overhead costs forovertime production are $5 per hour more than for normalproduction.