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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