Linear Programming, Course Quiz

In a linear programming problem, the conditions

x \ge 0

,

y \ge 0

are called

A corner points

B optimal solutions

C objective functions

D non-negativity constraints

Maximise

Z = 5x + 3y

subject to

3x + 5y \le 15

,

5x + 2y \le 10

,

x, y \ge 0

.

A

15

B

\displaystyle \tfrac{235}{19}

C

10

D

9

If the feasible region is bounded, then the objective function

Z = ax + by

A has a maximum but never a minimum

B has both a maximum and a minimum

C has infinitely many maxima always

D has no optimal value

Maximise

Z = x + 2y

subject to

x + y \le 5

,

x, y \ge 0

.

A

5

B

10

C

7

D

15

Minimise

Z = 3x + 5y

subject to

x + y \ge 2

,

x, y \ge 0

.

A

8

at

(1, 1)

B

6

at

(2, 0)

C

10

at

(0, 2)

D

0

at

(0, 0)

On a bounded feasible region,

Z

takes the values

0

,

18

,

24

and

15

at the four corners. The maximum of

Z

is

A

18

B

24

C

15

D

57

For an unbounded feasible region, a largest corner value

M

is the maximum of

Z = ax + by

only if

A

M

occurs at the origin

B the region contains the point

(M, M)

C

M

is positive

D the half-plane

ax + by > M

has no point in common with the feasible region

The corner points of the region

x + y \le 4

,

x, y \ge 0

are

A

(0, 0)

,

(2, 2)

,

(4, 4)

B

(0, 0)

,

(4, 0)

,

(0, 4)

C

(0, 0)

,

(4, 4)

D

(4, 0)

,

(0, 4)

only

Which point is feasible for

x + y \le 6

,

2x + y \le 8

,

x, y \ge 0

?

A

(4, 1)

B

(1, 6)

C

(2, 3)

D

(5, 1)

In a diet problem (meet nutrient needs at least cost), the nutrient constraints are usually of the form

A

> 0

only

B

\le

(at most the required amount)

C

=

only

D

\ge

(at least the required amount)

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