GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper

Question : 59 of 65

Marks: +1, -0

Two business owners Shweta and Ashok run their business in two different status. Each of them, independent of the other, produces two products A and B, sells them at 2,000 per kg and 3,000 per kg. respectively, and uses Linear Programming to determine the optimal quantity of A and B to maximize their respective daily revenue. Their constraints are as follows: i) for each business owner, the production process is such that the daily production of A has to be at least as much as B, and the upper limit for production of B is 10 kg per day, and ii) the respective state regulations restrict Shweta’s production of A to less than 20kg per day, and Ashok’s production of A to less than 15 kg per day. The demand of both A and B in both the states is very high and everything produced is sold.
The absolute value of the difference in daily (optimal) revenue of Shweta and Ashok is thousand Rupees(round off to 2 decimal places).

Your Answer:

Validate

Solution:

Let units of A = x
Let units of B = y
For Aakash.

X<15

Given

y ≤ 10

But

x ≥ y

10 ≤ x ≤ 15

Given above the feasible regions max. revenue will happen at

(15,10) ∴

max revenue =

14 × 2000+10 × 3000

......(i)
For Shweta

Let units of

A=X_{1}

Let units of

B=Y_{2}

Given

{X}_{2} ≤ 10 \& {X}_{1}<20 \& {X}_{1} ≥ {X}_{2} ≥ 10

x_{2} ≤ 10 \& 10 ≤ x_{1}<20

Maxima will occur at

(19,10)

. Max revenue

=19 × 2000+10 × 3000 . . . . . . . .

(ii)
Difference

=( {ii})-( {i})=5 × 2000=10000 {Rs} .=10

Thousands

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