Alex G.

asked • 02/11/17

I am trying to find what the maximum profit is?

A farmer has 110 acres on which to plant oats or corn. Each acre of oats requires $18 capital and 2 hours of labor. Each acre of corn requires $36 capital and 6 hours of labor. Labor costs are $8 per hour. The farmer has $2100 available for capital and $2400 available for labor. If the revenue is $51 from each acre of oats and $127 from each acre of corn, what planting combination will produce the greatest total profit? (Profit here is revenue plus leftover capital and labor cash reserve.) What is the maximum profit?

1 Expert Answer


Philip P. answered • 02/11/17

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Don L.

What you have will give the greatest revenue. Alex is looking for the greatest profit defined as revenue plus left over capital and labor cash reserve.
You will have to look at the revenue generated from each of the coordinates found based on your equation, P = $127x + $51y and then take into account the amount of capital and labor used for each solution. This will give you the greatest profit.
An example based on coordinates (0,110):
P = $5610. It would cost $1980 in capital leaving $120 capital remaining and $1760 in labor leaving $640 in labor remaining. The profit as defined, revenue + left-over capital + labor reserve would equal $6370.
The other coordinates would have to be used with the same calculations to find the maximum profit as defined.


Philip P.



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