Question

What point in the feasible region maximizes P for the objective function P = 2x + 3y? Constraints

2x+y≤15
x+3y≤20
x≥0,
y≥0 A. (0, 15) B. (5, 5) C. (8, 7) D. (2, 6)

Answer 1

Suppose 2x + y = 15 -----eq 1 . x + 3y = 20 -----eq 2. Multiplying eq (1) by 1 and (2) by 2 and subtracting the result We have: 2x + y = 15 and 2x +6y =40.If we subtract, we have y - 6y = 15 - 40. So we have -5y = -25. y is 5. Substiting into eq (1), we have 2x + 5 = 15. 2x = 15-5 =10 Hence X =5.Hence option B is the correct option.