How many pens and notebooks should she purchase in order to minimize her cost?

Question

Pam is going to buy at least 8 items for her back to school supplies. She is going to purchase pens and notebooks. She cannot use more than 5 pens or more than 6 notebooks. The pens she selected are $1.50 each and the notebooks are $0.75 each. How many pens and notebooks should she purchase in order to minimize her cost? 

Answer 1

Let x be number of pens and y be number of notebooks required to minimize the cost.

Cost function: z = 1.5x+0.75y

Constraints:

a) x +y >=8

b) x<=5

c) y<=6

d) x>=0

e) y>=0

On plotting the above constraint we get:

A(2,6)  B(5,6) and C(5,3) are feasible choice. And the region enclosed by triangle ABC is feasible region.

Now subjecting feasible choice to Z=1.5x +0.75y we get:

	X	Y	Z=1.5X+0.75Y
A	2	6	7.5  =MINIMUM
B	5	6	12
C	5	3	9.75

So, Pam should buy 2 pens and 6 notebooks in order to minimize her cost.