### 3 Answers

- 5 months ago
Obviously, the further to the right we go and the further up we go, the greater the value will be. The further left and further down we go, the smaller the value will be

6 * 1 + 8 * 1 = 6 + 8 = 14

The minimum value occurs at (1 , 1) and it's 14.

The maximum value will occur somewhere along the right-most border. So what we need to do is relate x to y and use a substitution to figure out where the maximum value occurs

x = 4 , y = 8

x = 5 , y = 2

(2 - 8) / (5 - 4) = -6/1 = -6

We need a line with a slope of -6 that passes through (4 , 8)

y - 8 = -6 * (x - 4)

y = 8 - 6 * (x - 4)

y = 8 - 6x + 24

y = 32 - 6x

f(x , y) = 6x + 8y

f(x , y) = 6x + 8 * (32 - 6x)

f(x , y) = 6x + 256 - 48x

f(x , y) = 256 - 42x

x is bounded between 4 and 5, so 256 - 42 * 4 will give us the greatest value of f(x , y)

256 - 42 * 4 = 256 - 168 = 88

Maximum value is 88

Math typo

6*4= 24

8*8= 64

24 + 64 = 88 (not 100)