Question

ABC company wishes to minimize its cost. Its cost is given by the equation C = 3x+4y. The business constraints are as follows:


`x + 2y \leq 14 \\3x - y \geq 0 \\x - y \leq 2`

Find a set of points (x, y) that will minimize the cost.

Answer 1

(2, 0)

Explanation:

To solve this problem, we have to plot a graph. A graph was plotted using geogebra online graphing calculator. From the attached graph we can see the points that satisfy the constraints: (0,0), (2, 0), (2, 6), (6, 4). But since x,y > 0, this leaves us with B(2, 6), C(2, 0), D(6, 4)

The cost equation is C = 3x + 4y

At point B(2, 6): C = 3(2) + 4(6) = 30

At point C(2, 0): C = 3(2) + 4(0) = 6

At point D(6, 4): C = 3(6) + 4(4) = 34

Therefore the minimum cost is at C(2, 0)