A candy manufacturer makes two types of special candy, say A and B. Candy A consists of equal parts of dark chocolate and caramel and Candy B consists of two parts of dark chocolate and one part of walnut. The company has in stock 430 kilograms of caramel, 360 kilograms of dark chocolate, and 210 kilograms of walnuts. The company sells Candy A for P285 and Candy B for P260 per kilograms. How much of each candy should the manufacturer produce to maximize profit?

If we let x as candy A

y as candy B

a as dark chocolate in candy a

b as dark chocolate in candy b

c as caramel

d as walnut

P as profit

we have the equations:

a + c = x

2b + d = y

a + 2b ≤ 360

c ≤ 430

d ≤ 210

P = 285x + 260y

This is an optimization problem which involves linear programming. It can be solved by graphical method or by algebraic solution.

P = 285 (a + c) + 260 (2b + d)

If we assume a = b

Then a = 120, 2b = 240

P = 285 (120 + 120) + 260 (240 + 120)

P = 162000

candy A should be = 240

candy B should be = 360