SOLUTION: A farmer has 120 acres of land on which she plans to grow wheat and corn. Each acre of wheat requires 5 hours of labor and $20 of capital, and each acre of corn requires 15 hours o

Let X be the area for wheat (in acres),  and
let Y be the area for corn.

The amount of labor is 5X + 15Y     hours.
The amount of capital is 20X + 30Y  dollars.

The constraints are 

 5x + 15Y <= 1500     (1)    (hours)
20X + 30Y <= 6000     (2)    (dollars)

X >= 0,               (3)
Y >= 0.               (4)

The profit function is P(X,Y) = 100X + 120Y.   (5)

So, the problem is to maximize (5) under restrictions (1) - (4). 


The feasibility area (1) - (4) is shown in the figure below.





Plots y =  (red)  and y =  (green)


The feasibility area is the intersection of two right-angled triangles: one with red hypotenuse (restrictions (1),(3),(4))
and the other with green hypotenuse (restrictions (2),(3),(4)).
The intersection is the smaller right-angled triangle,
and to get the solution of the minimax problems, you should compare the profit function at two points: (X,Y) = (0,100) and (X,Y) = (300,0).


P(0,100) = 100*0 + 120*100 = 12000 dollars,
P(300,0) = 100*300 + 120*0 = 30000 dollars.


The larger value is at the point (X,Y) = (300,0).
So the solution is (X,Y) = (300,0), i.e. 300 acres for wheat and 0 acres for corn.


The profit value expected/predicted is $30000.