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?

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

Can anyone help me?

Answer 2

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Answer 3

To maximize profits, Joely needs to determine the amount of each blend to make. Let's assume she makes x pounds of the breakfast blend and y pounds of the afternoon blend.

The weight constraint for the A grade tea is: x/3 + 1/2 y ≤ 45 pounds (since 1 pound of breakfast blend contains one third of a pound of A grade tea, and 1 pound of afternoon blend contains half a pound of A grade tea).
The weight constraint for the B grade tea is: 2/3 x + 1/2 y ≤ 70 pounds (since 1 pound of breakfast blend contains two thirds of a pound of B grade tea, and 1 pound of afternoon blend contains half a pound of B grade tea).

Now, let's formulate the profit equation. The profit from the breakfast blend is $1.50 per pound, so the profit for x pounds of the breakfast blend would be 1.50x dollars.
Similarly, the profit from the afternoon blend is $2.00 per pound, so the profit for y pounds of the afternoon blend would be 2.00y dollars.

To find the maximum profit, we need to optimize this objective function subject to the weight constraints.

Let's solve this mathematically using linear programming:

Objective function: Maximize Profit = 1.50x + 2.00y

Subject to:
1/3x + 1/2y ≤ 45
2/3x + 1/2y ≤ 70
x ≥ 0 and y ≥ 0

Now, we can graph these constraints on the x-y plane and find the feasible solution space. The feasible region will be the intersection of the shaded areas where the constraints hold true.

After finding the feasible region, we need to evaluate the objective function (the profit equation) at each corner point of the feasible region to determine the maximum profit.

Alternatively, you can use linear programming software or online calculators to solve this problem and find the exact values of x and y that maximize the profit.