Question

Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into 1 pound packages as follows:

A breakfast blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea, and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade tea.

If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on each pound of the afternoon blend, how many pounds of each blend should she make to maximize profits? What is the maximum profit?

Answer 1

Hence, (75,40) is the maximum point and maximum profit is $192.5

Explanation:

Let the breakfast be x

And let the lunch or afternoon be y

Inequalities will become

`(1)/(3)x+(1)/(2)y\leq 45`

`(2)/(3)x+(1)/(2)y\leq 70`

And objective function will be

Z=1.5x+2.0y

You can see the graph in the attachement

ABCD is the feasible region

Points of feasible region is (0,90) ,(0,0) ,(75,40) and(105,0)

We have to find Z by substituting the points of feasible region

At (0,90) we get

Z=1.5(0)+2(90)

Z=180

At (0,0)

Z=1.5(0)+2(0)

Z=0

At (75,40)

Z=1.5(75)+2(40)

Z=192.5

At (105,0)

Z=1.5(105)+2(0)

Z=157.5

The maximum number we are getting is 192.5 which is at (75,40)

Hence, (75,40) is the point of maximum