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A Farmer Wants to Maximize Area

Q: A farmer wants to put a fence around a vegetable garden. Only three sides must be fenced, since a rock wall will form the fourth side. If he uses 40m of fencing what is the maximum area possible?

A:  Okay, so we have two widths and one length.

The material used would . . . → Read More: A Farmer Wants to Maximize Area

Max/Min Problem, Difference of Two numbers

Q: Two numbers hava a difference of 16. Find the numbers if their product is a minimum.

A: Let x = first number Let y = second number

Equation 1: x-y = 16 Equation 2: xy=P , where P is the product.

You need to isolate for x or y in Equation 1, and . . . → Read More: Max/Min Problem, Difference of Two numbers

Max/Min Rectangle Problem, Maximize the Area

Q: You have 128 feet of fencing to fence a rectangular area. Find the largest possible area to enclose this amount.

A: The perimeter of the space will be 128=2w+2L, where w=width and L=length

Isolate for L: L=64-w

The formula for the area of the rectangle is A=w*L. Substitute L=64-w into the area formula . . . → Read More: Max/Min Rectangle Problem, Maximize the Area