Find the max value of c=6x-2y subject to the following constraints: x≥0 y≥0 x+2y≤14 4x-y≤20

Graph the equations or solve the system of equations to find the vertices within the shaded region.

x≥0, y≥0 represents the first quadrant.

x + 2y ≤ 14   ⇒  has intercepts (14, 0) and (0, 7).

4x - y ≤ 20  ; has intercepts (5, 0) and (-20, 0). Disregard (-20, 0) since it is not in Quadrant 1.

x + 2y ≤ 14 and 4x - y ≤ 20 intercept at (6,4).

Now evaluate the value (C) at the intercepts (0, 7), (5, 0), and (6,4).  Note: (14, 0) has been disregarded because it is outside of the shaded region.

C = 6x - 2y at (0, 7)  ⇒ C = 6(0) - 2(7)  ⇒  C = 0 - 14   ⇒  C = -14

C = 6x - 2y at (5, 0)  ⇒ C = 6(5) - 2(0)  ⇒  C = 30 - 0   ⇒ C = 30

C = 6x - 2y at (14, 0)  ⇒ C = 6(6) - 2(4)  ⇒  C = 36 - 8   ⇒  C = 28

The maximum value (C)  equals 30

maximum value is 30

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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i can't solve unless i know what the line is

step-by-step explanation:

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