A farmer has land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hoursof labor and $20 of capital, and each acre of corn requires 16 hours of labor and $40 of capital. Thefarmer has at most 800 hours of labor and $2400 of capital available. If the profit from an acre ofwheat is $80 and from an acre of corn is $100, how many acres of each crop should she plant tomaximize her profit?Let's finally answer the question. How many acres of wheat and corn should be planted? Fill inthe blanks (tip: all the answers should be whole numbers).The farmer should plantfor a maximum profit ofacres of wheat andacres of corn

A farmer has land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and $20 of capital. Each acre of corn requires 16 hours of labor and $40 of capital. The farmer has almost 800 hours of labor and $2400 of capital available. The profit from an acre of wheat is $80 and from an acre of corn is $100. We have to find the number of acres of each crop should she plant to maximize her profit.Let x be the number of acres of wheat and y be the number of acres of corn. Each acre of wheat requires 4 hours of labor and $20 of capital. Each acre of corn requires 16 hours of labor and $40 of capital. The farmer has almost 800 hours of labor and $2400 of capital available. wheat corn availability Labor 4 16 800 Capital 20 40 2400 The farmer has almost 800 hours of labor and $2400 of capital available. The objective function becomes z=800x+2400y. The linear programming problem becomes, max z=800x+2400y Subject to the constraints, 4x+16y≤80020x+40y≤2400.Use a graphical method to solve the problem, Consider the constraints as 4x+16y=800 x 0 200 y 50 0 And, 20x+40y=2400 x 0 120 y 60 0 Use these points to sketch the feasible region.Graph of the feasible region: The corner points are 0, 0, 0, 50, 40, 40, and 120, 0. Points Objective function value 0, 0 z=8000+24000=0+0=0 0, 50 z=8000+240050=0+120000=120000 40, 40 z=80040+240040=32000+96000=128000 120, 0 z=800120+24000=96000+0=96000 The maximum value is 128,000 which occurs at 40, 40.Final answer: The farmer should plant 40 acres of wheat and 40 acres of corn for a maximum profit of $128,000.