Question

NYC Mayor Bill de Blasio has to manage the supply budget for both the NYPD and hospitals. He can spend $50 per box of tear gas and batons for the NYPD. For a hospital, he spends $40 per box of protective gear that includes masks and other healthcare supplies. X represents the number of tear gas and batons boxes and Y represents the number of masks and healthcare supplies boxes. This month, there is an overall budget of $2,000. He also wants to purchase a minimum of 100 total supplies.

A) Write a key for the system of inequalities; defining the x and y variable.
B) Write a system of inequalities that could be used to represent the given scenario.
C) Assuming 45 boxes of tear gas are purchased, what is the maximum number of boxes of hospital supplies could he purchase that would fit the specified budget?
D) What would be your suggested amounts of X and Y variables for de Blasio? Explain how you determined these amounts? (Remember, there are multiple solutions to a system of inequalities, please explain why the solution you chose is the most viable.)(if you can't answer all of them, just answer like 2 or 3)

Answer 1

To write the key for the system of inequalities, define x as the number of tear gas and batons boxes purchased, and y as the number of masks and healthcare supplies boxes purchased. The system of inequalities can be written as: Cost Constraint: 50x + 40y ≤ 2000, Minimum Supplies Constraint: x + y ≥ 100. Assuming 45 boxes of tear gas are purchased, the maximum number of boxes of hospital supplies that can be purchased is 0.

Step-by-step explanation:

To write the key for the system of inequalities, we define:

• x: Number of tear gas and batons boxes purchased
• y: Number of masks and healthcare supplies boxes purchased

Now, let's write the system of inequalities:

• Cost Constraint: 50x + 40y ≤ 2000
• Minimum Supplies Constraint: x + y ≥ 100

Assuming 45 boxes of tear gas are purchased, the maximum number of boxes of hospital supplies that could be purchased is:

• Let x = 45
• Substitute this value into the cost constraint inequality: 50(45) + 40y ≤ 2000
• Simplify and solve for y: 2250 + 40y ≤ 2000
• Subtract 2250 from both sides: 40y ≤ -250
• Divide both sides by 40: y ≤ -6.25
• Since the number of boxes cannot be negative, the maximum number of boxes of hospital supplies that can be purchased is 0.

My suggested amounts of x and y for de Blasio would be:

• x = 50
• y = 50

I chose these amounts because they satisfy both the cost constraint and the minimum supplies constraint. Additionally, it provides an equal distribution of resources between the NYPD and hospitals.