Question

A bath shop sells two different gift baskets. The Pamper Me basket contains 1 bottle of shower gel, 3 bottles of bubble bath, and 4 candles and makes a profit of $14. The Best Friends basket contains 2 bottles of shower gel and 3 bottles of bubble bath and makes a profit of $12. Each week, the shop has 500 bottles of shower gel, 900 bottles of bubble bath, and 900 candles available. How many of each type of basket should the shop prepare each week to maximize profits? The shop should prepare Pamper Me baskets and Best Friends baskets. (Simplify your answers.)

Answer 1

To maximize profits, the shop should prepare 200 Pamper Me baskets and 150 Best Friends baskets each week.

Step-by-step explanation:

To maximize profits, we need to determine the number of each type of basket that should be prepared each week. Let's represent the number of Pamper Me baskets as 'x' and the number of Best Friends baskets as 'y'.

From the information given, we can form the following system of equations:

1x + 2y = 500 (equation 1)

3x + 3y = 900 (equation 2)

Multiplying equation 1 by 2, we get:

2x + 4y = 1000 (equation 3)

Now, subtracting equation 3 from equation 2, we can eliminate 'y' and solve for 'x':

(3x + 3y) - (2x + 4y) = 900 - 1000

x - y = -100

Adding equation 1 to the new equation gives:

(1x + 2y) + (x - y) = 500 - 100

2x = 400

x = 200

Substituting the value of 'x' back into equation 1, we can find 'y':

1(200) + 2y = 500

y = 150

Therefore, the shop should prepare 200 Pamper Me baskets and 150 Best Friends baskets each week.