Logo

AskSia

Plus

use statistics's method 13. Distribute the capital of 250000$250000 \$ among four com...
May 29, 2024
use statistics's method
Solution by Steps
step 1
Identify the given data from the table. The table provides the profit values for different capital investments across four companies (I, II, III, IV)
step 2
The total capital to be distributed is $250,000. We need to distribute this capital among the four companies to maximize the profit
step 3
Create a linear programming model to maximize the profit. Let x1,x2,x3,x4x_1, x_2, x_3, x_4 be the capital allocated to companies I, II, III, and IV respectively. The objective function to maximize is: Maximize P=0.17x1+0.25x2+0.20x3+0.30x4+0.38x1+0.40x2+0.35x3+0.45x4+0.50x1+0.48x2+0.52x3+0.50x4+0.55x1+0.56x2+0.60x3+0.55x4+0.60x1+0.62x2+0.68x3+0.68x4 \text{Maximize } P = 0.17x_1 + 0.25x_2 + 0.20x_3 + 0.30x_4 + 0.38x_1 + 0.40x_2 + 0.35x_3 + 0.45x_4 + 0.50x_1 + 0.48x_2 + 0.52x_3 + 0.50x_4 + 0.55x_1 + 0.56x_2 + 0.60x_3 + 0.55x_4 + 0.60x_1 + 0.62x_2 + 0.68x_3 + 0.68x_4 subject to the constraints: x1+x2+x3+x4=250,000 x_1 + x_2 + x_3 + x_4 = 250,000 0≤xi≤250,000 for i=1,2,3,4 0 \leq x_i \leq 250,000 \text{ for } i = 1, 2, 3, 4
step 4
Solve the linear programming problem using the simplex method or any optimization tool to find the optimal values of x1,x2,x3,x4x_1, x_2, x_3, x_4
Answer
The optimal capital distribution among the four companies to maximize profit is found using linear programming.
Key Concept
Linear programming for optimization
Explanation
Linear programming helps in distributing resources optimally to maximize or minimize an objective function subject to constraints.
© 2023 AskSia.AI all rights reserved