Acre is a

unit of area. Farmer Jones must determine how many acres of corn$-$and wheat to plant this year. An acre of wheat yields $25$ bushels of wheat and requires $10$ hours of labor per week. An acre of corn yields $10$ bushels of corn and requires $4$ hours of labor per week. All wheat can be sold at $$4$ a bushel, and all corn can be sold at $$3$ a bushel. Seven acres of land and $40$ hours per week of labor are available. Government regulations require that at least $30$ bushels of corn be produced during the current year. Let

$x_1=$ number of acres of corn planted, and

$x_2=$ number of acres of wheat planted.

$($a$)$ Using these decision variables, formulate an LP whose solution will tell Farmer Jones how to maximize the total revenue from wheat and corn.

$($b$)$ Solve the problem graphically.