Mathematics
milovukmartina
2016-04-09 20:47:27
If x and y are two nonnegative numbers and the sum of twice the first ( x ) and three times the second ( y ) is 60, find x so that the product of the first and cube of the second is a maximum.
ANSWERS
abireynolds14
2016-04-09 23:51:25

If we translate the word problems to mathematical equation,                                2x + 3y = 60 The second equation is,                               P = xy³ From the first equation, we get the value of y in terms of x.                                 y = (60 - 2x) / 3 Then, substitute the expression of y to the second equation,                               P = x (60-2x) / 3                             P = (60x - 2x²) / 3 = 20x - 2x²/3 We derive the equation and equate the derivative to zero.                            dP/dx = 0 = 20 - 4x/3 The value of x from the equation is 15. Hence, the value of x for the value of the second expression to be maximum is equal to 15.                                 

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