Question

Mr John Bennett has 240 acres to plant. He needs to decide how many acres of corn to plant and how many oats. He can make £40 per acre profit for corn and £30 per acre for oats. However, the corn takes 2 hours of labor per acre to harvest and the oats only take 1 hour per acre. He only has 320 hours of labor he can invest. To maximize his profit, how many acres of each should Mr Bennett plant?

Answer 1

Answer

COrn = 80 acres

Oats - 160 acres

Step-by-step explanation:

Answer 2

Given:

Mr John Bennett has 240 acres to plant. He needs to decide how many acres of corn to plant and how many oats. He can make £40 per acre profit for corn and £30 per acre for oats. However, the corn takes 2 hours of labour per acre to harvest and the oats only take 1 hour per acre. He only has 320 hours of labour he can invest.

To Find:

To maximize his profit, how many acres of each should Mr Bennett plant?

Solution:

First, we need to form the equation required in this question then we will observe the solution using a graph to see where we can get the maximum profit

The first equation we need is a maximising using equation which will be £40 per acre profit for corn and £30 per acre for oats.

                                             $Z=40x+30y$

where x is the variable for corn and y for oats similarly forming the subjective equations,

$x+y=240$ (total land we have)

$2x+y\geq 320$ (maximum labour we can allot)

Now plotting them into graph we can see that (80,)160 will give us maximum profit. therefore putting these values in the maximising equation,

$Z=40x+30y\\=40*80+30*160\\=8000$

Hence, the maximum profit Mr Bennett will get is $8000 at (80,160).