A restaurant owner has at most 100 pounds of ground beef which he can use for making hamburgers and slices of meat loaf. Each hamburger contains pound of ground beef and each slice of meat loaf contains pound of ground beef. He makes a profit of 10 cent on each hamburger, while he makes a profit of 15 cent on each slice of meat loaf. Labor cost for producing a hamburger and a slice of meat loaf are 5 cent and 12 cent, respectively. The restaurant owner wants the number of hamburgers made to be more or equal than the number of meat loaf. He also decided that the total number of hamburgers and meat loaf should be at least 50. If he is willing to pay at most $30 for the labor costs of producing these two items, find the number of hamburgers and the number of slices of meat loaf that will maximize his profits. 1) Determine the decision variables. 2) Determine the constraints. 3) Formulate a linear programming model. 4) Define: a) Optimum solution b) Optimum value c) Slack variable d) Range of Optimality e) Range of Feasibility f) Shadow Price g) Binding Constraints h) Non-binding constraints i) Feasible Region 5) Transform the linear programming model in (3) to standard form. 6 Using graphical method analyse the phrases defined in (4) 7) In graphical method analysis, when it comes to simultaneous changes for coefficients of objective function: a) Give one example where the optimal solution is applicable b) Give one example where the optimal solution is not applicable 8) In graphical method analysis, when it comes to simultaneous changes for RHS of constraints: a) Give one example where the shadow price is applicable b) Give one example where the shadow price is not applicable 9) Interpret all your finding correspond to the problem given.