Homework 1 Joe and Sons is a food processing plant that manufactures hot dogs and hot dog buns, they grind their own flour for the flour for the hot dogs at a maximum rate of 350 pounds per week. Each hot dog bun requires pound of flour. They currently have a contract with Pig land, Inc., which specifies hat a delivery of 700 pounds of pork product is delivered every Monday. Each hot dog requires 1/4 pound of pork product. All other ingredients in the hot dog buns are in plentiful supply. Finally, the labor force at Joe and Sons consists of six employees working full time (40 hours per week each). Each hot dog requires 3 minutes of labor, and each hot dog bun requires 1.5 minutes of labor. Each hot dog yields a profit of .21, and each bun yields a profit of .09. Joe and Sons would like to determine the number of hot dogs and hot dog buns to be produced each week. What is the linear programming model for this problem, optimal solution, binding constraints and how high could profit per hot dog be and still have same optimal solution