what planting combination will produce the greatest revenue?

[maggiemagnet]

A farmer has 100 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. The farmer has $2100 available for capital and 360 hours for labor. If the revenue is $55 from each acre of oats and $125 from each acre of corn, what planting combination will produce the greatest revenue?

I have to find the combination of corn and oats that gives the greatest revenue, so I think my variables should stand for acres of corn C and acres of oats O. C + O < 100, and C > 0 and O > 0.

The "capital" part gives me 18O + 36C < 2100 and the "labor" part gives me 2O + 6C < 360.

The revenue formula is F = 55O + 125C.

For my graph, I did O on the x axis and C on the y axis. When I graphed the lines, it looked like the line C = 60 - O/3 didn't actually make one of the sides of the shaded part. Did I do this wrong?

[DAiv]

For my graph, I did O on the x axis and C on the y axis. When I graphed the lines, it looked like the line C = 60 - O/3 didn't actually make one of the sides of the shaded part. Did I do this wrong?

Some restrictions may end up being superfluous. In this case, the line refers to the maximum amount that can be spent on labour, but that doesn't mean the farmer has to spend all that money.

Imagine if a millionaire owned the land. She has $1 million set aside for labour, but no combination of crops would ever use anything but a tiny fraction of that amount. As a result, the maximum labour line would be nowhere near the shaded area.

I did a quick sketch and my labour line doesn't form part of the shaded region, either.

I have to find the combination of corn and oats that gives the greatest revenue, so I think my variables should stand for acres of corn C and acres of oats O. C + O < 100, and C > 0 and O > 0.

The "capital" part gives me 18O + 36C < 2100 and the "labor" part gives me 2O + 6C < 360.

The revenue formula is F = 55O + 125C.

On a separate note, I'd recommend using a variable other than O for oats, as it is easily confused with the number zero. At first glance, your equations read as '180 + 36C < 2100', '20 + 6C < 360', and 'F = 550 + 125C'. The letter O may be discernable (with effort) when typed, but when handwritten, O and 0 may become indistinguishable.


DAiv

[maggiemagnet]

Thank you (and yes, "O" was confusing me, too!)