Youngkwon C. answered • 11/29/15

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Hi Ben,

If x and y represent the number of blocks and horses to be made, respectively.

The problem is to find out a pair of x and y to miximize

10x + 14y (Eq. 1)

under the set of conditions

x ≥ 0 (Eq. 2)

y ≥ 0 (Eq. 3)

2x + y ≤ 10 (Eq. 4)

x + 3y ≤ 15 (Eq. 5)

Out of 4 vertices from the region which satisfies Eq. 2 through Eq. 5,

the point (x, y) = (3, 4) maximizes Eq. 1.

The maximum profit is

10x + 14y = 10·3 + 14·4

= 30 + 56

= 86

when x = 3 and y = 4.

So, the manufacturer needs to make

**3 blocks**and

**4 horses**each day.