Question

Choose the Correct Feasible Region for the Following Constraints:

5X + 5Y < 80

2X + 6Y < 72

3X + 2Y < 42

X , Y > 0

Note: Some of these graphs look almost Identical, You will need to Create the Graph of the Feasible Region so you can Identify the Exact Corner Points.

Answer 1

Answer:

area = 122 sq unit

Step-by-step explanation:

Given constraints:

5X + 5Y < 80

2X + 6Y < 72

3X + 2Y < 42

X , Y > 0

To find the  co-ordinates we can find

$\dfrac{x}{16} +\dfrac{y}{16} <1\\\dfrac{x}{36} +\dfrac{y}{12} <1\\\dfrac{x}{14} +\dfrac{y}{21} <1$

the co-ordinates are shown in the diagram

by solving equation

5X + 5Y < 80

3X + 2Y < 42

we will get the intersection point x = 10 and Y = 5

shaded region in the graph shows the required region

required area can be found out by

$area = \int_{0}^{10}(16-x)dx+\int_{10}^{14}(21-1.5x)dx$

$area=\left ( 16x-\frac{x^2 }{2}\right)^{10}_0 +\left ( 21x-\frac{1.5x^2 }{2}\right)^{14}_{10}$

area = 122 sq unit