By graphing the system of constraints, find the values o f x and y that minimize the objective function.

x+2y=>8

x=>2

y=>0

minimum for C=x+3y

A. (8,0)

B. (2,3)

C. (0,10)

D. (10,0)

Graph the inequalities to find the vertices of the shaded region: (2, 3) and (8, 0).

Now, evaluate the the function C = x + 3y at those vertices to find the minimum value.

C = x + 3y at (2, 3) ⇒ C = (2) + 3 (3) ⇒ C = 2 + 9 ⇒ C = 11

C = x + 3y at (8, 0) ⇒ C = (8) + 3 (0) ⇒ C = 8 + 0 ⇒ C = 8

The minimum value occurs at (8, 0) with a minimum of C = 8

Answer: A

Option (A)

Step-by-step explanation:

Here, x + 2y = 8

c=x+3y

x≥2

y≥0

By considering the options (A) and (B)

For option (A)

x=8 and y=0

x+2y=8

put values of x and y in equation

8+2*0=8, which satisfies the equation

now c = 8+3*0=8

Now, for option (B)

x=2 and y=3

x+2y=8

put values of x and y

2+2*3=8, which satisfies the equation.

now c = 2+3*3=11

As we have to find the minimum value of c.

hence we take c=8

Hence, option (A) is correct.