operations management homework 1

Topics: Optimization, Linear programming, Constraint Pages: 7 (715 words) Published: March 10, 2014
Homework Assignment 2 Solution

Question 1: (True / False) (20 Points)
Answer this question in a table with the question number and the selected answer (True or False) in separate columns as shown below.

Question Number
Answer
1

2



10

Grading
2 points each

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. 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...
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