GRAPHS, FUR1 2004 VCAA 7 MC

The shaded region shown in the graph above (with boundaries included) represents the feasible region for a linear programming problem.
The maximum value of the objective function `y - 2x + 20`, for this feasible region, is

A. 18

B. 23

C. 25

D. 27

E. 33

Show Answers Only

`C`

Show Worked Solution

`text(Corner pts of feasible region)`

`(2, 9), (4, 11), (6, 10), (6, 1)`

`text(Let value) = V`

`V = y − 2x + 20 \ \ \ … \ text{(i)}`

`text(Check each corner pt)`

`text(Sub)\ (2, 9)\ text{into (i)}`

`V`	`= 9 − 2(2) + 20`
	`= 9 − 4 + 20`
	`= 25`

`text(Sub)\ (4, 11)\ text{into (i)}`

`V`	`= 11 − 2(4) + 20`
	`= 11 − 8 + 20`
	`= 23`

`text(Sub)\ (6, 10)\ text{into (i)}`

`V`	`= 10 − 2(6) + 20`
	`= 10 − 12 + 20`
	`= 18`

`text(Sub)\ (6, 1)\ text{into (i)}`

`V`	`= 1 − 2(6) + 20`
	`= 1 − 12 + 20`
	`= 9`

`:.\ text{Max value when (2,9) at 25.}`

`=> C`