Question

Student Enterprises sells two sizes of wall posters, a large 3- by 4-foot poster and a smaller 2- by 3- foot poster. The profit earned from the sale of each large poster is $3; each smaller poster earns $2. The firm, although profitable, is not large; it consists of one art student, Ahmed, at the University of Punjab. Because of her classroom schedule, Ahmed has the following weekly constraints: (1) up to three large posters can be sold, (2) up to five smaller posters can be sold, (3) up to 10 hours can be spent on posters during the week, with each large poster requiring 2 hours of work and each small one taking 1 hour. With the semester almost over, Ahmed plans on taking a three-month summer vacation to Lahore and doesn?t want to leave any unfinished posters behind. Find the integer optimal solution that will maximize her profit. Please show work and do not use any programs for this answer.

Answer 1

In order to find the optimal solution, we need to create a list of the constraint of the products. The following table sums it up:

Poster	Time	Max Unit Sold	Price per unit
Small	1	5	2
Big	2	3	3
Total	10

Then considering x and y units of small and big posters made, the constraints and the objective equations are the following:

Now the region of selection for this set of constraints is the following;

The region is the intersection of all the three regions ( red, blue and green). Now, the critical points and the value of the objective function is given below:

Critical Points	Objective function
(0,0)	0
(5,0)	10
(5,2.5)	17.5
(4,3)	17
(0,3)	9

Observe that since we are required to get a integer solution hence, the optimal solution would be to print 4 small and 3 large posters.