Question

I NEED SOMEONE TO DOUBLE CHECK WITH ME PLEASE..

Answer 1

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 2

Grade A = 45 lbs
Grade B = 70 lbs
Total weight = A + B = 45 + 70 = 115
Blend breakfast (M) = 1/3A + 2/3B
Blend afternoon (N) = 1/2A + 1/2B

Profit = 1.50 * lbs. Blend M + 2.00 * lbs. Blend N

Profit = 1.50 * (1/3A + 2/3B) + 2 .00/2A + 1/2B) =

45 pounds of A and 70 pounds of B yields max 24A + 72B = 98 Pounds Max M
max 38A + 76B = 114 Pounds Max N

The rate of profit for A is .50 per pound in M and 1.00 per Pound in N For B, rate of profit for B is 1.00 for M and 1.00 for N.

X = # pounds in A
Y = # pounds in B

115 = A + B

A = 115 - B

q = percent of M
r = percent of N

s = pounds of A in M then 45 - s = # pounds A in N
t = pounds of B in M and 70 - t = # pounds in N

.5s + 1.00 * (45-s) + 1.00(t) + 1.00(70-t) = p

1.5s + 2.00t = p

If s = 45 pounds then 70 = 70/45 = 14/9s pounds

.5s + 1(45-s) + 1(14/9s) + 1(70-14/9s) = p

5 * 45s + (45(1 - s)) + 14/9 * 45s + (45(1 - 14/9s) =p

22.5s + 45 - 45s + 70s + 35 - 70s = p

22.5s +70 - 115s = p

p = 137.5s + 70 p = 137.5

22.5 A and 45 B for M and 23.75 A and 23.75 B for N.
Max profit is $137.5

Answer 3

Anyone Please Help me check if i did the calculations correct Please.

Answer 4

@da_ScienceMan @rajat97 @hartnn

Answer 5

@Yacoub1993 I am trying to view d stuff u are solving! How do u calculate max profit?

Answer 6

its all shown above @da_ScienceMan

Answer 7

Yes I have looked at it up until when you started allocating 0.5 for A and 1 for B (since 1/3A + 2/3 ´B....=breakfast blend?)...all loooking as these are your assumptions, right?