Test: Linear Programming Level - 3 - Mechanical Engineering MCQ

Consider the following LPP

Max z = 2x₁ + 10x₂

s/t: 3x₁ + 2x₂ ≤ 4

5x₁ + 3x₂ ≤ 6

x₁ + x₂ ≤ 10

The solution for the above LPP is

Consider the following LPP

Minimize z = 5x₁ + 7x₂ + x₃

s/t: 2x₁ − x₂ + 4x₃ ≤ 10

x₁ , x₂ , x₃ ≥ 0

The solution for the above LPP is

Consider the following primal LPP. Find dual of the given primal.

Max: z = 4x₁ + 2x₂ + 6x₃

s/t: 2x₁ + 3x₂ + 2x₃ ≥ 6

3x₁ + 4x₂ ≤ 8

6x₁ − 4x₂ + x₃ ≤ 10

s/ t: 2y₁ + 3y₂ + 6y₃ ≥ 4

3y₁ + 4y₂ − 4y₃ ≥ 2

2y₁ + y₃ ≥ 6

y₁ , y₂, y₃ ≥ 0

s/t: − 2y₁ + 3y₂ + 6y₃ ≥ 4

−3y₁ + 4y₂ − 4y₃ ≥ 2

−2y₁ + y₃ ≥ 6

y₁ , y₂, y₃ ≥ 0

2y₁ + 3y₂ + 6y₃ ≤ 4

3y₁ + 4y₂ − 4y₃ ≤ 2

2y₁ + y₃ ≤ 6

y₁ , y₂, y₃ ≥ 0

s/t: − 2y₁ + 3y₂ + 6y₃ ≤ 4

−3y₁ + 4y₂ − 4y₃ ≤ 2

−2y₁ + y₃ ≤ 6

y₁ , y₂, y₃ ≥ 0

Find the initial basic feasible solution using VAM method.

A product is manufactured using two raw materials A and B. A is taken on x-axis and B is taken on Y-axis and the LPP is as follows.

Z_min = 2A + 3B

S⁄t ∶ 0.6 A + 0.3 B ≥ 45

0.1 A + 0.5B ≥ 25

A, B ≥ 0

Which of the following statement is correct?

Four workers are required to do four jobs. Time to complete every job is given in the table below

Find the minimum cost.

Find optimal assignment cost.

Consider the following profit matrix. Find the max profit

Consider the problem of assigning four sales persons to four different sales regions as given below. Find the maximum total sales?

All the values are given in thousands.

Consider the following problem A cost matrix is given, find the minimum total cost

Three workers (P, Q, R) are assigned to 3 machines (M₁ , M₂ , M₃ ) while operator Q cannot be assigned machine M₂ . Further, each operator is assigned to one machine and one machine requires only one operator. The operating cost is given for these operators in table below (in Rs). The minimum cost of assignment is ___________ (Rs).