Question

A farmer in Iowa owns 450 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields $2000 profit, requires three workers, and requires two tons of fertilizer. Each acre planted with corn yields $3000 profit, requires two workers, and requires four tons of fertilizer. There are currently 1000 workers and 1200 tons of fertilizer available.

a. Use Solver to help the farmer maximize the profit from his land.

b. Confirm graphically that the solution from part a maximizes the farmer’s profit from his land.

c. Use Solver Table to see what happens to the decision variables and the total profit when the availability of fertilizer varies from 200 tons to 2200 tons in 100-ton increments. When does the farmer discontinue producing wheat? When does he discontinue producing corn? How does the profit change for each 10-ton increment?

Answer 1

Answer:

Explanation:

the constrained variables are acres of wheat(let a) (cell I6) and acres of corn(let b) (cell J6)

Both the above constraints are positive and integer also

The land constraint of 400 i.e (I6+J6)<= 450 ="" is given="" by="" constraint=""><=l7 where k8="">

The fertilizer constraint of 1200 tons is given by K8<=l8 , where="" k8="">

The worker constraint of 1000 is given by K9<=l9 where k9="">

The variable to be maximized K5 is given by constraint K5=SUMPRODUCT(I5:J5,I6:J6)

b) Let a be the acres of wheat and b be the acres of corn.

so the constraints are

(a+b) <>

2a+4b<>

3a+2b <=1000 ="" ="" where="" a="">=0 and b>=0 and both a and b are integers

a is plotted on horizontal line and b is on vertical line

for 200 ton fertilizer the maximum profit occurs when 200 acres each are cultivated under wheat and corn.