A sports memorabilia store makes $6 profit on each football it sells and $5.50 profit on each baseball it sells. In a typical month, it sells between 35 and 45 footballs and between 40 and 55 baseballs. The store has no more than 80 footballs and baseballs in stock during the month. What is the maximum profit the store can make from selling footballs and baseballs in a month?

Question

A sports memorabilia store makes $6 profit on each football it sells and $5.50 profit on each baseball it sells. In a typical month, it sells between 35 and 45 footballs and between 40 and 55 baseballs. The store has no more than 80 footballs and baseballs in stock during the month. What is the maximum profit the store can make from selling footballs and baseballs in a month?

Answer 1

write down the data. If there are x footballs and y baseballs, then we have

p = 6x + 5.5y
35 <= x <= 45
40 <= y <= 55
x+y <= 80

we want to maximize p. Using your favorite linear optimization calculator, you find that

x=40
y=50
profit = 460

Answer 2

dang typo: y=40

Answer 3

To find the maximum profit, we need to determine the maximum number of footballs and baseballs the store can sell. Let's start with the footballs:

1. The store has no more than 80 footballs in stock.
2. The store can sell between 35 and 45 footballs in a month.
3. Therefore, the maximum number of footballs the store can sell is 45.

Now, let's move on to the baseballs:

1. The store has no more than 80 baseballs in stock.
2. The store can sell between 40 and 55 baseballs in a month.
3. Therefore, the maximum number of baseballs the store can sell is 55.

Next, let's calculate the maximum profit:

1. The store makes a $6 profit on each football and a $5.50 profit on each baseball it sells.
2. The maximum number of footballs the store can sell is 45, so the maximum profit from footballs is 45 * $6 = $270.
3. The maximum number of baseballs the store can sell is 55, so the maximum profit from baseballs is 55 * $5.50 = $302.50.
4. Therefore, the maximum profit the store can make from selling footballs and baseballs in a month is $270 + $302.50 = $572.50.

Answer 4

To find the maximum profit the store can make in a month, we need to consider the range of possible sales for footballs and baseballs and then calculate the profit for each possible combination of sales.

First, we determine the range of possible sales for footballs and baseballs. The store sells between 35 and 45 footballs and between 40 and 55 baseballs in a month.

To maximize profit, we want to consider the highest number of footballs and baseballs the store can sell within the given constraints.

Let's consider the upper ends of the ranges:
- If the store sells 45 footballs and 55 baseballs, the total profit from footballs would be 45 * $6 = $270, and the total profit from baseballs would be 55 * $5.50 = $302.50.
- Therefore, the maximum profit from this combination would be $270 + $302.50 = $572.50.

Now let's consider the lower ends of the ranges:
- If the store sells 35 footballs and 40 baseballs, the total profit from footballs would be 35 * $6 = $210, and the total profit from baseballs would be 40 * $5.50 = $220.
- Therefore, the maximum profit from this combination would be $210 + $220 = $430.

Therefore, the maximum profit the store can make from selling footballs and baseballs in a month is $572.50.

Please note that this calculation assumes that the store can sell all the available stock without exceeding the given limits.