The sum of a number and three times another number is 18. find the numbers if their product is a maximum.Please show all your work and explain the steps thank you! Write as quadratic eqaution plzz
akhildestan:
What u mean by product is maximum?
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Let the two numbers be X and Y respectively.
X + 3 Y = 18
X Y = K = their product.
X (18 - X) / 3 = K
18 X - X^2 = 3 K
We have to maximize the product K. So its differential is zero wrt to the variable X or Y.
d K / d X = 6 - 2 X / 3 = 0 => X = 9
Then Y = 3 and K = 27
X = 8, Y = 10/3 => K = 80/3 = 26.67
X = 10, Y = 8/3 => K = 80/3 = 26.67
d K/ dX is positive for X < 9 and is negative for X > 9. So Their product is maximum when X = 9.
X + 3 Y = 18
X Y = K = their product.
X (18 - X) / 3 = K
18 X - X^2 = 3 K
We have to maximize the product K. So its differential is zero wrt to the variable X or Y.
d K / d X = 6 - 2 X / 3 = 0 => X = 9
Then Y = 3 and K = 27
X = 8, Y = 10/3 => K = 80/3 = 26.67
X = 10, Y = 8/3 => K = 80/3 = 26.67
d K/ dX is positive for X < 9 and is negative for X > 9. So Their product is maximum when X = 9.
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