GRAPHS, FUR1 2002 VCAA 5 MC

The feasible region for a particular linear programming problem is shown shaded on the following graph. All relevant vertices are labelled.

The minimum value of the expression `4x -2y` for this feasible region is

A. –20

B. –10

C. 0

D. 22

E. 44

Show Answers Only

`A`

Show Worked Solution

`text(Boundary points:)`

`(0, 10), (2, 9), (8, 5), (11, 0), (0, 0)`

`text(Sub each boundary point into)\ 4x − 2y`

`text(Consider)\ (0, 10)`

`4(0) − 2(10) = text(–20)`

`text(This is the minimum value of all the`

`text(choices given in the answers.)`

`text((Similarly all other values of)\ 4x − 2y`

`text(can be calculated.))`

`=> A`