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?

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

Step-by-step explanation:

Let the breakfast be x

And  let the lunch or afternoon be y

Inequalities will become

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

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w