Solve using the graphical method.

Sunnydale Farms has a total of 240 acres of cropland.The farm owner wants to plant this acreage in corn and oats.An acre of corn brings $40 in profit, and an acre of oats gets $30 profit.A total of 320 labor-hours to raise the crops is available. Each acre of corn needs 2 labor-hours, and each acre of oats needs 1 labor-hour.The farm owner wants to optimize the planting of the 240 acres to make maximum profit.

(i)Which variable shouldxdefine?

a.total amount of profit made from planting corn, b.number of labor-hours for optimum oats planting,c.number of labor-hours for optimum corn planting, d.number of acres of corn planted

(ii)Which variable shouldydefine?

a.number of acres of oats planted, b.number of labor-hours for optimum oats planting, c.number of labor-hours for optimum corn planting, d.total amount of profit made from planting oats

(iii)Which of the following correctly defines the constraint on total acres of cropland available for planting?a.40x+30y240, b.2x+y320, c.x+y240, d.40x+30y320

(iv)Which of the following correctly defines the constraint on labor-hours available for farming?a.x+y240 b.x+y320 c.2x+y240 d.2x+y320

(v)Which of the following correctly defines the objective function?a.P=x+y. b.P=40x+30y. c.P=2x+y. d.P=320x240y

(vi)Which of the following sets of corner points correctly defines the feasible region for this system of linear inequalities?

a.(0,320);(80,160);(240,0). b.(0,240);(80,160);(160,0);(0,0). c.(0,240);(0,320);(80,160). d.(160,0);(240,0);(80,160)

(vii)Based on your determination of the feasible region for this business process, how many acres of corn and of oats should be planted to maximize profit?

a.160 acres of corn and 0 acres of oats. b.240 acres of corn and 0 acres of oats. c.80 acres of corn and 160 acres of oats. d.None of these answers are correct

(viii)Which of the following is the correct value for the amount of total maximum profit from raising the optimum acres of the two crops?

a.$8000. b.$9600. c.$7200. d.$6400