Managerial Decision Modeling w/ Spreadsheets, 3e (Balakrishnan/Render/Stair)
Chapter 4 Linear Programming Sensitivity Analysis
4.1 Chapter Questions
1) Surplus is typically associated with which type of constraints?
A) ≤
B) ≥
C) =
D) ≠
E) ±
Answer: B
Page Ref: 124
Topic: Sensitivity Analysis Using Graphs
Difficulty: Easy
2) Assume that the shadow price of a non-binding "≤" constraint is 5. This implies that:
A) if the right-hand side value of the constraint increases by 1 unit, the objective function value will increase by 5 units
B) if the right-hand side value of the constraint increases by 1 unit, the objective function value will decrease by 5 units
C) if the right-hand side value of the constraint increases by 1 unit,
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Each week there are 300 pounds of material 1; 400 pounds of material 2; and 200 hours of labor. The output of product A should not be more than one-half of the total number of units produced. Moreover, there is a standing order of 10 units of product C each week.
Formulation
Max 10A + 10B + 10C
Subject to: 3A + B + 5C ≤ 300 (constraint #1) 2A + 4B ≤ 400 (constraint #2) 4A + 2B + 3.5C ≤ 200 (constraint #3) C ≥ 10 (constraint #4) A, B, C ≥ 0
9) Which constraints are binding?
A) 1 and 2
B) 1 and 4
C) 2 and 3
D) 3 and 4
E) 2 and 4
Answer: D
Page Ref: 130
Topic: Sensitivity Analysis Using Graphs
Difficulty: Easy
10) What is the optimal objective function value?
A) 925
B) 825
C) 100
D) 92.5
E) none of the above
Answer: A
Page Ref: 130
Topic: Sensitivity Analysis Using Graphs
Difficulty: Easy
11) By how much would the profit contribution of product A has to increase before it will be profitable to produce A?
A) $20
B) $0
C) $1E+30
D) $132.5
E) $10
Answer: E
Page Ref: 130
Topic: Sensitivity Analysis Using Graphs
Difficulty: Easy
12) Suppose that we force the production of one unit of product A. The new objective function value will be
A) $925
B) $915
C) $935
D) $900
E) Not enough information is provided.
Answer: B
Page Ref: 130
Topic: Sensitivity Analysis Using Graphs
Difficulty: Challenging
13) Suppose that the production manager has an additional 100 pounds of material 1. What impact will this have on the
11. If 8,000 units are produced, what is the total amount of manufacturing overhead cost incurred to support this level of production? What is the total amount expressed on a per unit basis?
c. Explain how the location of each curve graphed in question 7b would be altered if (1) total fixed cost had been $100
* The variances are due to the Mile High Cycle company not forecasting for increased production. The company budgeted for the production of 10,000 cycles but the actual production was 10,800 units. When the company increased production, the production efficiency decreased. The company had to use or rework parts that added extra cost to the expenses; the reworked parts added $25,000 of extra expenses to the wheel assembly production and $45,000 to the final assembly process. The material,
The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.
ABC Company is a manufacturing firm that specializes in making cedar roofing and siding shingles. The current annual sales of the company are roughly $1.2 million. This is a 25% increase from the previous year. The goal of this company is to reach $3 million in annual sales within the next 3 years. The CEO has decided to expand the product line to include an additional product. The product expansion consists of manufacturing cedar dollhouses using shingle scrap materials. A product expansion will result in additional revenue and gross profit to help reach the goal of $3 million in annual sales but there are many factors that need to be considered before moving forward
Problem b) 50 cents increase in unit transportation cost between plant A and region 2
If Darby Company drops the shipping limitations and allows any distribution center to supply to any customer zone for which they have shipping information, their total cost would be reduced to $600,942, which is a savings of $19,828 or 3.2%. By putting the above information into the objective function, the distribution plan without restrictions reduces the cost of shipping to $177,712 – a savings of $16,888. In addition, this new plan allows the company produce more of its meters at its more cost efficient San Bernardino plant – in fact, under this plan it produces at capacity, which is 20,000 units, meaning that its cost of manufacturing is $200,000. These units are then shipped to Las Vegas. The El Paso plant produces 14520 units for the Ft. Worth center and only 6740 for the Santa Fe center. The cost of manufacturing these units are $152460 and $70,770 respectively, making the cost at the El Paso plant $223,230. Adding all these costs together gives us the total cost as such: $177,712 + $200,000 + $223,230 = $600,942. This plan allows more than one center to supply to a specific zone and the solution shows that this is the case for the San Diego customer zone. The Santa Fe center supplies 620 units to them and the Las Vegas center supplies the other 3,840, satisfying their 4460 demanded units. In addition, this plan allows a
5. Suppose that in part (1) management specified the objective of maximizing the total number of printers produced each shift rather than total profit contribution. With this objective, how many units of each printer should be produced per shift? What effect does this objective have on total profit and workload balancing?
1.1 Chuck Sox makes wooden boxes in which to ship | motorcycles. Chuck and his three employees invest a total of 40 | hours per day making the 120 boxes. | a) What is their productivity? | | Total hours invested in production=40 hours per day | | produced number of boxes in a day=120 | | | | Productivity per day is =units produced/input used | | productivity per day is =120 boxes/40 hours | | productivity per day = 3 boxes per day | | | | their producivity is 3 boxes per day | | | b)
c) faces a constrained cost minimization problem in both the short run and the long run.
A shorter range indicates a more sensitive variable (concerning the objective function coefficients). The shortest ranges we found was that of the Qty of Fabric 1 manufactured on dobbie and also the Qty of Fabric 1 purchased. This indicated that these variables are most sensitive to change. This is evident as shown in the addition of a 9th dobbie loom. Note that the overall Profit margin did not increase significantly. However, the Qty of Fabric 1 manufactured on the dobbie loom and purchased varied drastically between the 8 dobbie loom run and the 9 dobbie loom run.
Q.1 Compute the following quantities for the current production process as well as for Mike’s and Ike’s plans, assuming the plans are implemented as described in the case. (50 points)
The firm's best level of output is OK which is sold at unit cost OP. The total revenue of the firm is equal to the area OPNK. The total cost of producing OK quantity of output is equal to OTSK. The firm is suffering a net loss equal to the shaded area PTSN.
A company manufactures a single product in its factory utilizing 600% of its capacity. The selling price and cost details are given below: