Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Expert Solution & Answer
Chapter 5.3, Problem 6P
Explanation of Solution
Calculating the extra payment:
- Let x1 tons of steel 1 is produced, x2 tons of steel 2 produced and x3 tons of steel 3 is produced.
- In order to maximize the profit, the following Linear
Programming has to be solved: - max z=
- Such that
- The output of this Linear Programming is given below:
- max z=
- Subject to constraint
- End
- LP optimum is found at step 3
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QUESTION 2
CU, Incorporated (CUI), produces copper contacts that it uses in switches and relays. CUI
needs to determine the order quantity, Q, to meet the annual demand at the lowest cost. The
price of copper depends on the quantity ordered. Annual demand is 25,000 kilograms per
year. Holding cost is 20 percent per unit per year of the price of copper and the Ordering cost
is $30.00. Table 2 that follows, shows the quantity discount schedule price-break:
Table 2- Quantity Discount Schedule
Quantity (kg)
5,000 and greater than 5,000
3,750 to 4,999
2,500 to 3,749
1,250 to 2,499
1 to 1,249
Price ($)
0.38
0.39
0.40
0.41
0.42
Determine the optimal order size that you would order if you were purchasing copper from
CUI.
3.
A company is considering opening warehouses in four cities: New York, Los Angeles, Chicago, and
Atlanta. Each warehouse can ship 100 units per week. The weekly fixed cost of keeping each warehouse
open is $400 for New York, $500 for Los Angeles, $300 for Chicago, and $150 for Atlanta. Region 1 of
the country requires 80 units per week, region 2 requires 70 units per week, and region 3 requires 40
units per week. The costs (including production and shipping costs) of sending one unit from a plant
to a region are shown in Table 3. We want to meet weekly demands at minimum cost, subject to the
preceding information and the following restrictions:
1.
If the New York warehouse is opened, then the Los Angeles warehouse must be opened.
2.
At most two warehouses can be opened.
3.
Either the Atlanta or the Los Angeles warehouse must be opened.
Formulate an IP that can be used to minimize the weekly costs of meeting demand.
Table 3
To ($)
From
Region 1
Region 2
Region 3
New York
20
40
50
Los…
3. National Disc Corp. produces the discs used in producing Xbox and PlayStation discs. Their
local plant runs 24 hours a day, 7 days a week. In a given day, there are requirements for the
total number of employees that must be at the plant. These are given below.
Employees Needed
Hours
12am - 4am
4am - 8am
8am-12pm
12pm - 4pm
4pm - 8pm
8pm-12am
8
10
16
21
18
12
Employees can either work 8-hour or 12-hour shifts, starting at the times stated above (12-
hour shifts can start only at 12 am/pm or 8 am/pm). Those working 8-hour shifts cost the
company $40 per hour in benefits, and those working 12-hour shifts cost the company $60
per hour. Develop a linear program that can be used to determine how National should
staff the local plant so as to minimize labor costs (you do not need to solve the model).
Be sure to clearly identify your variables.
Chapter 5 Solutions
Operations Research : Applications and Algorithms
Ch. 5.1 - Prob. 1PCh. 5.1 - Prob. 2PCh. 5.1 - Prob. 3PCh. 5.1 - Prob. 4PCh. 5.1 - Prob. 5PCh. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - Prob. 5P
Ch. 5.2 - Prob. 6PCh. 5.2 - Prob. 7PCh. 5.2 - Prob. 8PCh. 5.3 - Prob. 1PCh. 5.3 - Prob. 3PCh. 5.3 - Prob. 4PCh. 5.3 - Prob. 5PCh. 5.3 - Prob. 6PCh. 5.3 - Prob. 7PCh. 5.3 - Prob. 9PCh. 5.3 - Prob. 10PCh. 5.3 - Prob. 11PCh. 5 - Prob. 1RPCh. 5 - Prob. 2RPCh. 5 - Prob. 3RPCh. 5 - Prob. 4RPCh. 5 - Prob. 6RPCh. 5 - Prob. 7RPCh. 5 - Prob. 8RPCh. 5 - Prob. 9RPCh. 5 - Prob. 10RPCh. 5 - Prob. 11RPCh. 5 - Prob. 12RPCh. 5 - Prob. 13RPCh. 5 - Prob. 14RPCh. 5 - Prob. 15RPCh. 5 - Prob. 16RP
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