Question

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

Answer 1

Answer:

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.

Answer 2

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