Linear Programming

[jshaziza]

A farm consists of 240 acres of crop land. The farmer wishes to plant part or all of the acreage in corn or oats. The profit per acre in corn production is $40, and that in oats is $30. An additional restriction is that the total hours of labor during the production is no more than 320. Each acre of land in corn production uses 2 hours of labor during the production period, but production of oats requires only 1 hour per acre. How many acres of land should be planted in corn and how many in oats in order to maximize profit?

So far I have P=40c +30o, h< or equal to 320, o>or equal to 0, c>or equal to 0. However I don't think I have all the linear inequalities, could someone please tell me what others I have missed? Thanks.

 

[galactus]

Let x=acres of corn and y=acres of oats.

They want to plant part or all, so \(\displaystyle x+y\leq{240}\)

P=40x+30y

Labor: \(\displaystyle 2x+y\leq{320}\)


Objective value=8000
x=80
y=160

I will leave the calculations up to you.