If there were multiple positive X's it would be simple to test.

Right away you can discard the negative answer because X is a length and you cannot have negative length, so X=2√(130). Next, set dc/dx equal to 0 this will allow you to find the x value for all mins and maxes in the original equation. Simply isolate the Y variable on one side of the first equation so you can substitute the expression it's equal to into the second equation.Ĭhange the 6240/x to 6240X^-1 to make deriving easier. To move on you need a single equation with only 2 variables. You can then assign the $6 cost to one variable and the $4 cost to the other. Perimeter is equal to twice the length + twice the width. the cost of the materials is going to be determined by the perimeter of the space. You also know that c is the combined cost of the materials. X=width of the space, Y=length of the space, and C=cost of materials.īecause you know that the area is 780 square feet, you know that 780 is the product of x and y.

Optimization calculus khan academy