Algebra 2..?

Question

Find the min and max vaules of the objective function subject to the giving constraints.

Objetive function: C= x + 4y
Constraints:
x > or equal to 2
x< or equal to 5
y> or equal to 1
y< or equal to 6

thank you

Answer 1

Assuming I know what you're asking...

Put in the minimum values of x and y to find the min value of C, then put in the max values of x and y to find the max value of C

so...

C = 2 + 4(1) = 6 (min value)
C = 5 + 4(6) = 29 (max value)

so... 6

Answer 2

Find the min and max vaules of the objective function subject to the giving constraints.

Objective function: C= x + 4y
2 ≤ x ≤ 5
1 ≤ y ≤ 6

All you need do is test the corners as this is a classic linear programming situaton

So min (C) will occur when x = 2 and y = 1 (min x and y)
ie min (C) = 6

Max C will occur when x = 5 and y = 6 (max x and y)

ie max (C) = 29

So, with the defined constraints, 6 ≤ C ≤ 29

Answer 3

The objective function is C = x + 4y.

If we rearrange the given constraints we have:
2 < x < 5
1 < y < 6

Now it's easy.

The maximum value of C is at (x,y) = (5,6).
The minimum value of C is at (x,y) = (2,1).

max C = 5 + 4*6 = 29
min C = 2 + 4*1 = 6