Answer:
Costs are reduced when you have 3 ounces of brand A and 4 ounces of brand B for a cost of 39 cents / serving.
Explanation:
Yes:
x = ounces of brand A
y = ounces of brand B
The objective function and restrictions will be as follows:
Minimize cost function, C = 5x + 6y
This function is subject to:
x + y <= 10
3x + 5y> = 29 eq. 1
4x + 2y> = 20 eq1.2
x, y> = 0
We need to graph the constraints. First, x, y> = 0 their axes meet at x and y as limits. x + y <= 10 is a line from (0.10) to (10.0) and is equal to the area below the graph. The equation 3x + 5y> = 29 passes through (0.5.8), (29 / 3.0) and is equal to the area on the line. 4x + 2y> = 20 passes from (0,10), (0,5) and is equal to the area on the line.
The limits are delimited by (0.10), (10.0), (29 / 3.0). Solving the equations:
12x + 20y = 116 (multiplying eq. 1 by 4)
-12x - 6y = -60 (multiplying eq. 2 by -3)
14 y = 56
y = 4
4x + 8 = 20
x = 3
Replacing in the objective equation:
C = 5 (0) + 6 (10) = 60
C = 5 (29/3) + 6 (0) = 48.33
C = 5 (10) + 6 (0) = 50
C = 5 (3) + 6 (4) = 39
Costs are reduced when you have 3 ounces of brand A and 4 ounces of brand B for a cost of 39 cents / serving.
