## Linear Programming Problems

1. A farmer has 10 acres to plant in wheat
and rye. He has to plant at least 7 acres. However, he has only $1200
to spend and each acre of wheat costs $200 to plant and each acre of
rye costs $100 to plant. Moreover, the farmer has to get the planting
done in 12 hours and it takes an hour to plant an acre of wheat and 2
hours to plant an acre of rye. If the profit is $500 per acre of
wheat and $300 per acre of rye how many acres of each should be
planted to maximize profits?

2. A gold processor has two sources of
gold ore, source A and source B. In order to kep his plant running,
at least three tons of ore must be processed each day. Ore from
source A costs $20 per ton to process, and ore from source B costs
$10 per ton to process. Costs must be kept to less than $80 per day.
Moreover, Federal Regulations require that the amount of ore from
source B cannot exceed twice the amount of ore from source A. If ore
from source A yields 2 oz. of gold per ton, and ore from source B
yields 3 oz. of gold per ton, how many tons of ore from both sources
must be processed each day to maximize the amount of gold extracted
subject to the above constraints?

3. A publisher has orders for 600 copies of a certain text from San Francisco and 400 copies from Sacramento. The company has 700 copies in a warehouse in Novato and 800 copies in a warehouse in Lodi. It costs $5 to ship a text from Novato to San Francisco, but it costs $10 to ship it to Sacramento. It costs $15 to ship a text from Lodi to San Francisco, but it costs $4 to ship it from Lodi to Sacramento. How many copies should the company ship from each warehouse to San Francisco and Sacramento to fill the order at the least cost?