Question

Bowie State University magazine agency wants to determine the best combination of two possible magazines to print for the month of May.  Star which the University has published in the past with great success is the first choice under consideration. Prime is a new venture and is a promising magazine. The university envisages that by positioning it near Star, it will pick up some spillover demand from the regular readers. The University also hopes that the advertising campaign will bring in a new type of reader from a potentially very lucrative market. The publishing department wants to print at most 500 copies of Star and 300 copies of Prime. The cover price for Star is $3.50, the university is pricing Prime for $4.50 because other magazines doing the same line of business command this type of higher price. The University publishing department has 25 hours of printing time available for the production run. It has 27.5 hours for the collation department, where the magazines are actually assembled. Each copy of Star magazine requires 2.5 minutes to print and 3 minutes to collate. Each Prime requires 1.8 minutes to print and 5 minutes to collate. How many of each magazine should BSU print to maximize revenue? Show all the corner solutions and the value of the objective function.

Hint: You are required to maximize revenue assuming that Star = X and Prime = Y. create a table, specify the LP, draw graph to show feasible region and solve for the corner points. Find the profit for each of the solutions. Also convert hours to minutes in the constraints. The problem has 4 constraints excluding the non-negative constraints.

a. Formulate a linear programming model for this problem.

b. Represent this problem on a graph using the attached graph paper. Show the feasible region.

c. Solve this model by using graphical analysis showing the optimal solution and the rest of the corner points as well as the profits

Answer 1

Decision Variables which are to be found from the problem

Let us assume that X stands for Number of Star magazine and Y stands for Number of Prime magazines

The objective function will be maximisation of revenue

Z maximise = 3.5 X+4.5Y

where 3.5 is the revenue from one star and 4.5 is the revenue from 1 prime

Subject to

The constraints

1. At most 500 copies of Star means = X 500

2. Similarly Y 300

3. 25 hours of printing means 1500minutes and 2.5 minute for Star and 1.8 inute for prime means

2.5X+1.8Y 1500

4. similarly 27.5 hours for collation and star requires 3 minutes and Ptime requires 5 minutes means

3X+5Y 1650

also the non negativity conditions

For constrains we will have the table First 2 constraint will be straight lines parallel to the X and Y axes

For constraints 3 and 4 give value as zero for X and Y and find the other values

contrain 1	X= 500	Parallel to Y axis
Constraint2	Y= 300	Parallel to X axis
2.5X+1.8Y=1500	X=0, Y=833.33	Y=0 X=600
3X+5Y=1650	X=0 Y=330	Y=0 X=550

With this we can draw the graph which is attached below

Then shading down wards as all inequality is less than or equal to we have to shade the graoh twards left and below we will get the corner values as

A(0,0), B(300,0) C(0,330) and D(300, 150)

Applying values of X and Y from A,B,C and D we get

For A Z= 0

For B Z= 1050

For C Z= 1485And For D Z= 172