Choose the Correct Feasible Region for the Following Constraints: 5X + 5Y < 80 2X + 6Y < 72 3X + 2Y < 42 X , Y > 0Note: 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.
Accepted Solution
A:
Answer:area = 122 sq unitStep-by-step explanation:Given constraints:5X + 5Y < 802X + 6Y < 723X + 2Y < 42X , Y > 0To find the co-ordinates we can find [tex]\dfrac{x}{16} +\dfrac{y}{16} <1\\\dfrac{x}{36} +\dfrac{y}{12} <1\\\dfrac{x}{14} +\dfrac{y}{21} <1[/tex]the co-ordinates are shown in the diagramby solving equation5X + 5Y < 803X + 2Y < 42we will get the intersection point x = 10 and Y = 5shaded region in the graph shows the required regionrequired area can be found out by[tex]area = \int_{0}^{10}(16-x)dx+\int_{10}^{14}(21-1.5x)dx[/tex][tex]area=\left ( 16x-\frac{x^2 }{2}\right)^{10}_0 +\left ( 21x-\frac{1.5x^2 }{2}\right)^{14}_{10}[/tex]area = 122 sq unit