Question

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 the University print to maximize revenue? Show all the corner solutions and the value of the objective function.

Shows work please!

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. (15 points)

b. Represent this problem on a graph using the attached graph paper. Show the feasible region. (10 points)

c. Solve this model by using graphical analysis showing the optimal solution and the rest of the corner points as well as the profits. (25 points)

Answer 1

a) Formulated LPP:

Objective Function:

Max Z = 3.50 X + 4.50 Y

Subject to :

2.5 X + 1.8 Y <= 1500 ....Printing time constraint .......(1)

3 X + 5 Y <= 1650 ...........Collation time constraint .......(2)

X <= 500 ........................ Print copies constraint ...........(3)

Y <= 300 ........................ Print copies constraint ............(4)

X >= 0, Y >= 0 .............. Non negative constraints

(b) LPP in graph with shaded feasible region

c)

Solving LPP by Graphical method:

As per feasible region, Maximum profit happens at two points:

i) Intersection of constraints 2 & 4

ii) Intersection of constraints 2 & 3

	x	y
	3.5	4.5	Profit/ unit
	x-coordinate	y-coordinate	Total Profit
Solving 2 & 4	50	300	1525
Solving 2 & 3	500	30	1885	Max Profit

LPP Solution:

Each magazine should the University print to maximize revenue is as below;

Star = 500 copies

Prime = 30 copies

Which gives optimum Max Profit = 1885

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