A farmer has a 40-acre farm. The farmer is trying to determine how many acres of corn, peanuts, and cotton to plant. The farmer has a contract to supply at least 10 acres worth of corn and 2 acres worth of peanuts to a distributor. Each crop requires labor, fertilizer, and pesticide for successful growth. Each acre of corn provides $400 in profit. Each acre of peanuts provides $375 in profit. Each acre of cotton provides $450 in profit. The labor requirements for each acre of crop are as follows: 2 hours for corn; 3 hours for peanuts; 2 hours for cotton. The fertilizer requirements for each acre of crop are as follows: 4 bags for corn; 3 bags for peanuts; 2 bags for cotton. The pesticide requirements for each acre of crop are as follows: 3 gallons for corn; 2 gallons for peanuts; 4 gallons for cotton. There are 320 hours of labor, 140 bags of fertilizer, and 90 gallons of pesticide available. How many acres of each crop should be planted to maximize profit? What is the maximum profit?

DIRECTIONS

1) Create the basic linear programming model (i-system). Type it!

2) Convert the i-system to an e-system. Type it!

3) Type the preliminary (if needed) and initial simplex tableaus. Label all columns!

4) Apply the simplex method and type ALL simplex tableaus needed to solve the question. Label all columns!

-Could you please post all tableaus and the final answers