The minimum value of z=4x + 10y subject to:
3x+y> or equal to 24
6x+4y> or equal to 66
x> or equal to 0, y> or equal to 0 is:

• first constraint; let value of y be 0, then the value of x=24÷3=8 so values 1(x, y)=(8, 0) and when x is 0, the value of y will be 24 thus value 2 of x, y will be =(0, 24).
  For the second constraint, let y be 0, then x=66÷6=11. So the first values of x, y will be (11, 0) and when x is 0, y will be =66÷4=16.5 thus value 2 will be (0, 16.5). But when substituting the value respectively in ach equation, the values (11, 0) doesn’t conform to constraint 1 and values (0, 24) doesn’t conform with constraint 2 hence eliminated. Thus valid vales remaining are (8, 0) and (0, 16.5). Thus z = 4x + 10y
  Z=8(4) +0=32
  =0+16.5(10) =165
  Hence minimum value is 32
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