1) You plan a meal with the following ingredients and requirements:
| bread | potatoes | meat | beans | eggs | butter | requirement | ||
| units | lb | lb | oz | lb | number | oz | ||
| cost | $1.89 | $0.75 | $0.48 | $2.29 | $0.15 | $2.85 | ||
| calaries | 280 | 250 | 43 | 78 | 160 | 300 | 2200 | at least |
| vitamin A | 5 | 15 | 37 | 20 | 12 | 0 | 300 | at least |
| vitamin c | 0 | 70 | 0 | 50 | 0 | 0 | 60 | at least |
| protein | 3 | 5 | 40 | 12 | 10 | 0 | 80 | at least |
| fat | 8 | 2 | 25 | 3 | 18 | 30 | 50 | at least |
a. Find the cheapest meal that satisfies all the requirements. What are the ingredients and what is the total cost.
b. Find the integer solution to this problem.
c. Can you use these results?
2) You have three plants that produce a certain type of boats. The capacity for next month is 38 in San Diego, 45 in Santa
Ana, and 58 in San Jose. Production cost per boat is $1,065 in San Diego, $1,005 in Santa Ana, and $975 in San Jose.
Demand for next month is 42 in Newport Beach, 33 in Long Beach, 14 in Ventura, 10 in San Luis Obispo, and 22 in San
Francisco. The shipping costs per boat are summarized in the following table:
| Shipping | Cost | to: | |||
| From | NB | LB | VEN | SLO | SF |
| SD | $200 | $220 | $280 | $350 | $400 |
| SA | $125 | $125 | $280 | $350 | $400 |
| SJ | $390 | $365 | $300 | $250 | $100 |
Develop a production and shipping schedule that minimizes the total cost of production and shipping while satisfying all
the demand.
3) You own a wheat warehouse with a capacity of 20 thousand bushels. At the beginning of month 1, you have 6 thousand
bushels of wheat. Each month, wheat can be bought and sold at the prices per one thousand bushels shown in the table
below.
The sequence of events during each month is as follows:
You observe your initial stock of wheat.
You can sell any amount of wheat up to your initial stock at the current month’s selling price.
You can buy as much wheat as you want, subject to the warehouse size limitation.
Determine how to maximize the profit earned over the next 10 months by finding the quantities to sell and buy each
month. What is your profit?
| selling price | purchase price | |
| month 1 | $3 | $8 |
| month 2 | $6 | $8 |
| month 3 | $7 | $2 |
| month 4 | $1 | $3 |
| month 5 | $4 | $4 |
| month 6 | $5 | $3 |
| month 7 | $5 | $3 |
| month 8 | $1 | $2 |
| month 9 | $3 | $5 |
| month 10 | $2 | $5 |
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