GRAPHS, FUR1 2005 VCAA 8 MC

For the shaded region above (with boundaries included), the value of the objective function `text(P) = 4x – 3y` is a
maximum at the point

A. (0, 0)

B. (0, 100)

C. (50, 100)

D. (90, 60)

E. (120, 0)

Show Answers Only

`E`

Show Worked Solution

`text(Consider)\ A`

`text(Sub)\ (0, 0)\ text(into P) = 4x − 3y`

`text(P)`	`= 4(0) − 3(0)`
	`= 0`

`text(Consider)\ B`

`text(Sub)\ (0, 100)\ text(into P) = 4x − 3y`

`text(P)`	`= 4(0) − 3(100)`
	`= text(−300)`

`text(Consider)\ C`

`text(Sub)\ (50, 100)\ text(into P) = 4x − 3y`

`text(Consider)\ D`

`text(Sub)\ (90, 60)\ text(into P) = 4x − 3y`

`text(Consider)\ E`

`text(Sub)\ (120, 0)\ text(into P) = 4x − 3y`

`text(P)`	`= 4(120) − 3(0)`
	`= 480`

`:.\ E\ text(has max value.)`

`=> E`