A farmer in Napa Valley has a 100-acre farm

A farmer in Napa Valley has a 100-acre farm on which to plant grapes or almonds. Every acre planted with grapes requires 75 gallons of water per day. Every acre planted with almonds requires 100 gallons of water per day. The farmer estimates that it will take 1.5 hours of labor to harvest each acre planted with grapes and 3 hours to harvest each acre planted with almonds. They believe that the grape yield will sell for about $3,000 an acre and that the almond yleld will sell for about $4,000 an acre. The farmer can pump a maximum of 9,000 gallons of water per day for irrigation purposes from their own well. Finally, the farmer can hire laborers to harvest the fields at a rate of $10 per hour. The laborers are all capable of harvesting either grapes or almonds. The farmer has only saved $2,400 from last year for paying laborers. If the farmer sells all the grapes and almonds that they produce, how many acres of each crop should the farmer plant in order to maximiże profits?

1. Find the optimal solution by setting up the problem in Excel and using the “Solver” Add-in.

Solution

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