Laura is the fund-raising manager for a local charity. She is ordering caps for an upcoming charity walk. The company that makes

$125,060,000

one-hundred twenty-five million, and sixty thousand dollars

Also, 125.06 expressed as a fraction is 6253/50, if that representation is acceptable.

You can refer to it as 125.06 million dollars when using the figure from the prompt.

Begin by disregarding the inequality symbol and substituting it with an '=' sign. After that, determine the x- and y-intercepts.

15x + 10y = 1,100

x-intercept:

15x + 0 = 1,100

x = 1,100/15 = 73.33

y-intercept:

0 + 10y = 1,100

y = 1,100/10 = 110

Now, plot the points (73.33,0) and (0,110). Given that the inequality symbol is ≥, representing equality, connect these points using a solid line. 

Next, let's identify a point on the graph, for instance, the origin (0,0). Use this point in the equation.

15x + 10y ≥ 1,100

15(0) + 10(0)? 1,100

0? 1,100

0 < 1,100

This makes the ≥ statement false. As a result, the alternate area defined by the line is the solution. Consequently, shade that region. The resulting graph is displayed in the attached image.

She ought to select the monthly plan for unlimited movies instead of paying $2.99 per film. This choice is advisable because if she continues paying this amount for each individual movie, her total monthly costs will rise significantly. For example, if she has 8 days off in a month (on Saturdays and Sundays) and pays for each film on those days, the total expense would exceed that of the unlimited monthly plan priced at $7.99. And that doesn't include other potential viewing days or any public holidays that could allow her to watch more movies.

Answer:

The highest number of long-sleeved shirts that can be ordered is 8

and

The lowest number of long-sleeved shirts that can be acquired is 0

Step-by-step breakdown:

Let y denote the quantity of short sleeves and x indicate the quantity of long sleeves.

According to the stipulated conditions:

Members of a school club are purchasing coordinating shirts. They understand that a minimum of 25 members will opt for a shirt.

therefore, we have;

               or

....[1]

Given that long-sleeved shirts are priced at $10 each and short-sleeved shirts at $5 each.

Thus;

The total expense for long sleeves amounts to 10x and

the total cost of short sleeves is 5y

Moreover; the club has a budget that does not exceed $165

therefore;

 

  or

......[2]

By plotting the inequality functions:

Graphing equations [1] and [2] produces a maximum at the coordinates (8, 17)

thus, x= 8.

Taking the minimum value of x =0 results in y falling between 25 and 33.

consequently, the solution space is situated between the intersecting lines to the left.

In conclusion, a maximum of 8 long-sleeved shirts can be obtained, while the minimum number of long-sleeved shirts that can be bought is 0