Formulate a linear programming model to this problem.

Solve the linear programming model formulation in Problem 15 for the Patel brothers graphically.
a. How many acres of land was cultivated at the optimal solution? Did they use all the land?

b. If they plant only onions, what would be their maximum profit? 

c. If they obtain 20 acres of additional land, will the mix of crop at the optimal solution change?

Data From Problem 15

Patel brothers have 50 acres of farmland on the banks of River Ganges. They plan to grow tomatoes and onions. Since onions requires less water, the irrigation authority wants the brothers to cultivate at least 25 acres of land with onions. Brothers work in their farm themselves to reduce the cost of plantation. Besides, the government provides the seeds and other farming equipment for free. Even then, they need ₹500 per acre to plant tomatoes and ₹800 per acre to plant onions. The brothers have ₹30,000 now. They earn a profit of ₹6,000 from an acre of tomatoes and ₹4,000 from an acre of onions. The brothers want to know how many acres of land is to be planted with tomatoes (x₁) and onions (x₂) to maximize their revenue.