apps of linear programming: A Farmer has a choice of planti

[tretre]

Question: A Farmer has a choice of planting a combination of 2 different crops on 20 acres of land. The seed of crop A costs $120 per acre and crop B is $200 per acre. The government restricts crop A to 15 acres but there is no restriction for crop B. Crop A takes 15 hours per acre at $5.60 an hour and crop B takes 10 hours per acre at $5.00 an hour. The estimated income for crop A is $600 per acre and the estimated income for crop B is $520 per acre. How would the farmer distribute the 20 acres of land to both the crops to get the maximum profit?

The only problem I have with this type of problem is writing the inequalities. I don't know where to start and I just need help writing the inequalities. From there, I can do the rest.

 

[arthur ohlsten]

let x = acres of crop A and 20-x acres of crop B x<15

profit of crop A=${ 600- [$120+ $15[5.6]] } x
profit of crop A= ${600-120 - 84}x
profit crop A = $396 x

profit crop B=${520-50-200}[20-x]
profit crop B=$270[20-x]

total profit =396x+270[20-x] in dollars x<15
total profit = 5400+ 126x x<15 equation of a straight line

total profit is maximum when x is a maximum
set x=15
plant 15 acres crop A,and 5 acres in crop B

 

[tretre]

oh ok . . i got it now . . thank you !!