Two business owners Shveta and Ashok run their businesses in two different states. Each of them, independent of the other, produces two products A and B, sells them at Rs. 2,000 per kg and Rs, 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 Shveta’s production of A to less than 20 kg 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 Shveta and Ashok is ________ thousand Rupees (round off to 2 decimal places)

The correct answer is 10.

To understand why, let us formulate and solve the Linear Programming Problem (LPP) for both business owners, Shveta and Ashok.

Let the daily production quantities of product A and product B be $x_1$ kg and $x_2$ kg, respectively.
The selling prices of product A and product B are Rs. 2,000 per kg and Rs. 3,000 per kg, respectively. Since everything produced is sold, the objective of both owners is to maximize their daily revenue, represented by:
Maximize $Z=2000x_1+3000x_2$

Constraints for both business owners:
1. The daily production of A has to be at least as much as B:
$x_1\ge x_2$
2. The upper limit for production of B is 10 kg per day (i.e., B can be produced up to 10 kg):
$x_2\le 10$
Additionally, production quantities must be non-negative: $x_1\ge 0$, $x_2\ge 0$.

1. Shveta's Optimal Revenue:
State regulations restrict Shveta's production of A to less than 20 kg per day. In the context of maximizing revenue with continuous limits, we consider the boundary condition:
$x_1\le 20$
To maximize the objective function $Z=2000x_1+3000x_2$, we want to make $x_2$ as large as possible because it has a higher coefficient (3000 vs 2000).
The maximum possible value for $x_2$ is 10 (since $x_2\le 10$).
Since $x_1\ge x_2$, and we want to maximize both variables, the optimal production occurs at the upper bounds:
$x_1=20$ and $x_2=10$ (which satisfies $20\ge 10$).
Evaluating Shveta's maximum revenue:
$Z_{\text{Shveta}}=2000\left(20\right)+3000\left(10\right)=40000+30000=\text{Rs.}70000$

2. Ashok's Optimal Revenue:
State regulations restrict Ashok's production of A to less than 15 kg per day:
$x_1\le 15$
Similarly, to maximize revenue, we choose the maximum values within the feasible region.
The maximum value for $x_2$ is 10, and the maximum value for $x_1$ is 15 (which satisfies $15\ge 10$).
Evaluating Ashok's maximum revenue:
$Z_{\text{Ashok}}=2000\left(15\right)+3000\left(10\right)=30000+30000=\text{Rs.}60000$

Absolute Difference in Daily Revenue:
The difference between Shveta's and Ashok's optimal daily revenues is:
$\text{Difference}=70000-60000=\text{Rs.}10000$

Since the question asks for the difference in thousand Rupees:
$\frac{10000}{1000}=10$