1.Find two numbers whose difference is 160 andwhose product is a minimum.

smaller number: largernumber:

2.Find two positive numbers whose productis 25 and whose sum is a minimum. (If both values are thesame number, enter it into both blanks.)

smaller number: largernumber:

3.Find the dimensions of a rectangle withperimeter 108 m whose area is as large as possible. (Ifboth values are the same number, enter it into bothblanks.)

smaller value: largervalue:

4.Find the dimensions of a rectangle witharea 1,000 m² whose perimeter is as smallas possible. (If both values are the same number, enter it intoboth blanks.

smaller value: m larger value:m

5.If 30,000 cm² of material isavailable to make a box with a square base and an open top, findthe largest possible volume of the box.

ans:

6.A box with a square base and open top must have avolume of 4,000 cm³. Find the dimensions ofthe box that minimize the amount of material used.

sides of base: height: