A community farm has 4000 square kilometers of land available to plant wheat (X) and millet (Y).
Question:
A community farm has 4000 square kilometers of land available to plant wheat (X) and millet (Y). Each kilometer square of wheat requires 10 gallons of fertilizer and insecticide and 1 hour of labor to harvest. Each square kilometer of millet requires 4 gallons of fertilizer and insecticide and 2 hour of labor to harvest. The community has at most 30,000 gallons of fertility and insecticide and at most 5000 hours of labor for harvesting. If the profits per square kilometer are $60 for wheat and $40 for millet, how many square kilometers of each crop should the community plant in order to maximize profits? What is the maximum profit? Hint: x is the number of square kilometers of wheat and y is the number of square kilometers of millet.
There are three constraints and one is redundant.
| Constraints | Wheat (X) | Millet (Y) | Maximum requirements |
| Fertilizer and insecticide | 10 | 4 | 30,000 |
| Labor | 1 | 2 | 5,000 |
| Profit | $60 | $40 |
a) Specify the linear program
b) Draw a graph to show the corner points and identify the redundant constraint.
c) Solve for the maximum amounts of wheat and millet that can be produced.
| Corner points | Wheat (X) | Millet (Y) | Profit |
| A | |||
| B | |||
| C | |||
| D |
Expert Answer:
answer Linear Programming for Community Farm a Linear Program Objective Function Maximize Profit Z 6... View the full answer
