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You have a nice place in a rural setting with a little kitchen and a few cows out in the back. You figure you can make $3 profit per cake (C) that you can bake or $3 profit per dozen cookies (D) you make. The main constraints for you are that you can only use the oven in the kitchen nine hours per day (and the oven will only fit one cake or one dozen cookies at one time), and you can only have 10 pounds of butter per day. Each cake takes 0.75 hours to bake and requires one half pound of butter. A dozen cookies require 0.50 hours in the oven and one pound of butter. You want to maximize profit from production. 1. How many variables are there in a linear programming problem to maximize profit from making cakes and cookies? 2. How many constraints are there in a linear programming problem to maximize profit from making cakes and cookies (excluding the non-negativity constraints)? 3. How many cakes and how many cookies should be made in this profit maximizing situation and what is the maximum profit? 4. What is the range of optimality for each profit contribution? 5. What is the range of feasibility for the nine hours of kitchen time and the 10 pounds of butter?
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