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2.19 (Based upon Carino and LeNoir) WellBuilt Cabinet Co. owns a cabinet manufacturing facility that not only makes cabinets but also produces the wood panels or "blanks" used. The wood used to produce blanks come from cither logs that are milled and dried within the company or lumber boards that are purchased either dried or green (undried). All undried wood is dried in the company's kilns. The logs can be purchased in any of four diameters, each producing different amounts of blanks. The lumber boards can be purchased in one of the two grades. Pricing, yield, and availability for all log diameters and lumber grades are given in the tables below.

Log Diameter       Cost/Log      Blanks/Log      Max Logs      Boardft/Log
8                               100                70                     100                400
10                              120                90                     75                  600
14                              150                120                   60                  1000
18                              175                150                   40                  1400

Lumber Grade       Dried      Green    Blanks/Board Foot    Max Board Feet
1                               1.85         1.60                0.15                           4000
2                               1.15         1.0                  0.06                         10000

WellBuilt needs to produce at least 2000 blanks per week, but its mill can handle at most only 50 logs and its kiln can dry at most 2500 board feet of lumber. Formulate and solve a linear program that allows WellBuilt to meet its demands while minimizing cost.

2.20 During the next 4 months your company must meet (on time) the following demands for plastic garbage cans: 3000 large and 2500 small in month 1; 4500 large and 4000 small in month 2; 3000 large and 4000 small in month 3; and 4000 large and 4000 small in month 4. At the beginning of month 1, 75 large 50 small cans are on hand. Each can is produced from plastic bought
another and firm and must go through two different areas before month, are automatically shipped 30,000 pounds of Those you cans not sold in a given month must be stored in cans. facility. Below are the requirements for producing and storing addition to its production cost per unit.

Can       Plastic (lb)       Machine       Painting       Storage Units       Production       Storage
Large    5                            0.1                0.05             6                            15                     2
Small    3                            0.8                0.04             3                            10                     1
                  
There are 650 machine hours and 350 painting hours available each month, as well as 10,000 units of storage available. Production in a given month can be used to meet that month's demand. Formulate and solve a linear program to determine the optimal production schedule.

2.22 Fitness Sneaker Company manufactures and sells (you guessed it) sneakers. During each of the next 6 months, it forecasts the following demands (pairs of sneakers).

Month            1             2          3          4          5          6
Demand      6000      5000    8000    4000    7000    5000

All demand must be met during that month. Each sneaker is made by workers and requires 20 minutes per pair. Each worker works 200 hours per month and can work up to 40 hours of overtime per month. Workers are paid a salary of $3000 per month, plus $75 per hour of overtime. Prior to each month's production. Fitness Sneaker can either hire additional workers or lay off some of its current workers. Due to administrative and other expenses, it costs $2000 to hire a worker and $3000 to fire a worker. Currently, at most 3000 pairs of sneakers can be stored in inventory, and this number is calculated at the end of the month (after all production). Each stored pair costs $5 per month in storage fees. If there are 15 workers and 1000 pairs of sneakers in storage at the beginning of month 1. determine how Fitness Sneaker can minimize its cost of meeting the demand.

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Operations Research Problems
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