463 Words2 Pages

This unit was about a bakery that made two different types of cookies, they made plain cookies and frosted cookies. The problem given to us was to find out how many of each type of cookie that bakery should make per day. We were given a couple of constraints that we had to follow for this problem. The first constraint was the amount of cookie dough they had. They only have 110 pounds of cookie dough to use each day. Then we were giving the fact that they only have 32 pounds of icing per day. The last two constraints that we were given was the fact they we only had enough oven space to make 140 dozen cookies and they only had 15 hours to make all of their cookies.
The formula’s we arrived at for constraints were based of those facts and these here. Plain cookies require 1 pound of cookie dough to make (per dozen), as well as .1 hours (per dozen). Iced cookies use .7 pounds of cookie dough and .4 pounds of icing (per dozen) as well as .15 hours to make (per dozen).
So when you combine the two of those you end up with these constraints: Oven Space Available P + I ≤ 140 Amount of Cookie Dough Available P + .7I ≤ 110 Amount of Icing Available I ≤ 80 Preparation Time Available P + 1.5I ≤ 150
Those formula’s I used to create the constraints with are called equivalent inequalities. An equivalent inequality means that there is a number of different answers to a problem not just one. Such as the problem X < 5 means that any number less than 5 would be a correct solution.
Linear Inequalities are when you take your equivalent inequality and put it on a graph. So you would take X < 5 and make it X = 5, graph that line and then shade your half plane. In order to know which half of the plane you need to shade you simply need to plug in one point. My suggestion is to plug in the point (0,0) because its the easiest point to plug in (no multiplication

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