Operations management homework free essay sample

1- The feasible solution space only contains points that satisfy all constraints. 2- Graphical solution to linear programming problems can handle problems that involve any number of decision variables. 3- The value of an objective function decreases as its iso-objective line is moved away from the origin. 4- If a single optimal solution exists to a graphical LP problem, it will exist at a corner point. 5- Using the enumeration approach, optimality is obtained by evaluating every coordinate (or point) in the feasible solution space. 6- A non-unique solution to a linear program indicates the existence of more than one optimal point with different values of the decision variables but the same value of the objective function. 7- An unbounded solution to a linear programing problem is usually due to omitting a constraint. 8- If a linear programming model has no feasible solution space, then the answer to that model is a unique optimal solution. We will write a custom essay sample on Operations management homework or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page 9- The constraint x1 = 2 x2 is non linear. 10- In the general diet problem, the objective function is a maximization of profit obtained from selling the foods. Answer Question Number Answer 1 T 2 F 3 F 4 T 5 F 6 T 7 T 8 F 9 F 10 F Question 2: (40 Points) LP model formulation and computer solution Problem statement A group of scouts is spending a few days in a remote hostel where the only foods available are the ones listed in the table below. After consulting with a nutritionist, the group leader learned that a satisfactory diet has at least 2000 kcal of energy, 55g of protein, and 800 mg of calcium. The nutritionist also recommended supplementing with pills of vitamin and iron, which are available for free in the hostel. Since some of the scouts would be happy to subsist on 10 servings of beef and beans, the leader has decided to impose variety by having a limit on the number of servings/day for each of the six foods. The leader of the group wants to minimize the cost of feeding his group while satisfying minimum nutrition requirements. Food Serving Size Energy (Kcal) Protein (g) Calcium (mg) Price Cents/serving Limit Serving /day Oatmeal 28g 110 4 2 3 4 Chicken 100g 205 32 12 24 3 Eggs 2 Large 160 13 54 13 2 Whole Milk 237CC 160 8 285 9 8 Cherry Pie 170g 420 4 22 20 2 Beef Beans 260g 260 14 80 19 2 Required a. Formulate a linear programming model to minimize the cost per scout per day. (20 Points) b. Solve the using Excel Solver. The formulas in the LHS of the constraint must be formatted correctly for copying down. (15 Points) c. Print the solution sheet and the formula sheet formatted according to the standard computer printout requirements. Make sure your name is in the heading of each sheet. (5 Points). Answer Decision Variables x1 = Number of Oatmeal servings per day to feed to each scout. x2 = Number of Chicken servings per day to feed to each scout. x3 = Number of Eggs servings per day to feed to each scout. x1 = Number of Whole Milk servings per day to feed to each scout. x2 = Number of Cherry Pie servings per day to feed to each scout. x3 = Number of Beef Beans servings per day to feed to each scout. *** Another correct answer is to model decision variables per gram, egg, etc. In that case, for the rest of the model, the numbers have to be divided by the serving size. Except for the serving / day that has to be multiplied by serving size. *** Oatmeal Chicken Eggs Whole Milk Cherry Pie Beef Beans Serving Size 28g 100g 2 Large 237CC 170g 260g Energy (Kcal) 110 205 160 160 420 260 Protein 4 32 13 8 4 14 Calcium (mg) 2 12 54 285 22 80 Price Cents/serving 3 24 13 9 20 19 Limit Serving /day 4 3 2 8 2 2 Objective function min 3 x1 + 24 x2 + 13 x3+ 9 x4 + 20 x5+19 x6 Constraints Energy110 x1 + 205 x2 + 160 x3+ 160 x4 + 420 x5 +260 x6 = 2200 Protein4 x1 + 32 x2 + 13 x3+ 8 x4 + 4 x5 +14 x6 = 55 Calcium2 x1 + 12 x2 + 54 x3+ 285 x4 + 22 x5 +80 x6 = 800 Serving Limit for Oatmeal x1 = 4 Serving Limit for Chicken x1 = 3 Serving Limit for Eggs x1 = 2 Serving Limit for Whole Milk x1 = 8 Serving Limit for Cherry Pie x1 = 2 Serving Limit for Beef Beans x1 = 2 Non- Negativity x1, x2, x3, x4, x5, x6 = 0 Computer Solution: See the file Scouts. xlsx Question 3: (40 Points) Graphical Solution Approach Given the linear program Max 3X1 + 4 X2 S. t. Cons1-1X1 + 2 X2