Chapter 1: An Introduction to Management Science<\/p>\n
Question 1 (5 points): Micromedia offers computer training seminars on a variety of topics. In the seminars each student works at a personal computer, practicing the particular activity that the instructor is presenting. Micromedia is currently planning a two-day seminar on the use of Micro- soft Excel in statistical analysis. The projected fee for the seminar is $600 per student. The cost for the conference room, instructor compensation, lab assistants, and promotion is $9600. Micromedia rents computers for its seminars at a cost of $120 per computer per day.<\/p>\n
Solution <\/p>\n
Question 2 (5 points): Preliminary plans are under way for the construction of a new stadium for a major league baseball team. City officials have questioned the number and profitability of the luxury corporate boxes planned for the upper deck of the stadium. Corporations and selected individuals may buy the boxes for $300,000 each. The fixed construction cost for the upper- deck area is estimated to be $4,500,000, with a variable cost of $150,000 for each box constructed.<\/p>\n
a)<\/p>\n
the profit on each box is $(325,000 -150,000 )=$175000<\/p>\n
so to cover the $4,500,000 fixed cost you need<\/p>\n
so, there are 26 boxes <\/p>\n
b)<\/p>\n
The marginal revenue from a one-unit increases in sales is $325,000<\/p>\n
The marginal cost (variable cost per box) is $175,000<\/p>\n
which indicates a marginal profit of $175,000 for each additional box sold.<\/p>\n
Since marginal profit is positive, and all 47 boxes can be sold<\/p>\n
it is recommended to build all 47 boxes.<\/p>\n
The total profit = 175000(47) \u20134,500,000 = <\/p>\n
$3725000<\/p>\n
Chapter 2: An Introduction to Linear Programming<\/p>\n
Question 3 (6 points):: Reiser Sports Products wants to determine the number of All-Pro (A) and College (C) footballs to produce in order to maximize profit over the next four-week planning ho- rizon. Constraints affecting the production quantities are the production capacities in three departments: cutting and dyeing; sewing; and inspection and packaging. For the four-week planning period, 340 hours of cutting and dyeing time, 420 hours of sewing time, and 200 hours of inspection and packaging time are available. All-Pro footballs provide a profit of $5 per unit, and College footballs provide a profit of $4 per unit. The linear programming model with production times expressed in minutes is as follows:<\/p>\n
A portion of the graphical solution to the Reiser problem is shown in Figure. <\/p>\n
a) Feasible region is shaded in the graph\u00a0<\/p>\n
B) Coordinates of extreme points and the corresponding profit are listed<\/p>\n
A C Z<\/p>\n
Intersection of C1 and A-axis 1,700 0 8,500<\/p>\n
Intersection of C2 and C-axis 0 1,680 6,720<\/p>\n
Intersection of C2 and C3 800 1,200 8,800<\/p>\n
Intersection of C1 and C3 1,400 600 9,400<\/p>\n
Point (1400, 600) generates the maximum profit<\/p>\n
c) profit line (objective function(z)) is drawn on the graph.<\/p>\n
d) Which constraints are binding? Explain<\/p>\n
Constraints c1 and c3 are binding, because optimal solution lies at their intersection.<\/p>\n
Now the solution point changes to intersection of C2 and C3.<\/p>\n
A = 800, C = 1200<\/p>\n
Profit = 9200<\/p>\n
Question 4<\/p>\n
Solve the following linear programming problem using the graphical solution procedure:<\/p>\n
Max 5A + 5B<\/p>\n
s.t. <\/p>\n
1A \u2264 100 <\/p>\n
1B \u2264 80 <\/p>\n
2A + 4B \u2264 400<\/p>\n
A, B \u22650Let c = 5a + 5b<\/p>\n
We are going to maximize c.<\/p>\n
Now take the constraint equations…<\/p>\n
a < 100<\/p>\n
When graphed, this will be the region to the left of the straight line a = 100 and excluding the points lying on the line a = 100. We shade this region.<\/p>\n
b < 80<\/p>\n
When graphed, this will be the region below the straight line b = 80and excluding the points lying on the line b = 80. We shade this region.<\/p>\n
2a + 4b < 400 => a + 2b < 200<\/p>\n
First we graph the line a + 2b = 200<\/p>\n
To do this, we take points (0, 100) and (200, 0), which lie on the line.<\/p>\n
Now, putting x = 0, y = 0 (Test Point), we see that 0 + 0 < 200 is TRUE<\/p>\n
Therefore, we shade the region which contains the origin.<\/p>\n
The intersection of all the shaded regions is the feasible or solution region.<\/p>\n
The maximum value of c lies at one of the corners of the feasible region.<\/p>\n
The corners have the coordinates: (40, 80) and (100, 50)<\/p>\n
Plug in all these values in c = 5a + 5b. We see that maximum value of c occurs when<\/p>\n
a = 100, b = 50<\/p>\n
The maximum value of c is 5(100) + 5(50) = 750.<\/p>\n
Question 7. The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year\u2019s program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown.<\/p>\n
To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized.<\/p>\n
Question 8<\/p>\n
Question 8. The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor utilization, and product profitability:<\/p>\n
Solutions <\/p>\n
Question 9:Consider the following all-integer linear program:<\/p>\n
Max 1×1 + 1×2 <\/p>\n
s.t.4×1 + 6×2 \u226422 <\/p>\n
1×1 +5×2 \u226415 <\/p>\n
2×1 + 1×2 \u2264 9<\/p>\n
x1, x2 \u2265 0 and integer<\/p>\n
a)<\/p>\n
B&c)<\/p>\n","protected":false},"excerpt":{"rendered":"
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