U3P2 - Optimization Review

A farmer wants to construct a rectangular pigpen using 300ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

A supermarket employee wants to construct an open-top box from a 14 by 30 inch piece of cardboard. To do this, the employee plans to cut out squares of equal size from the four corners so the four sides can be bent upwards to create the box. What size should the squares be in order to create a box with the largest possible volume?

An open topped box is being constructed from a 50 by 20 inch piece of cardboard by cutting squares out of equal size from the four corners so the four sides can be bent upwards to create the box. What size should the squares be in order to create a box with the largest possible volume?