Use Mathematical Models Involving Linear Inequalities

question 67

Multiple Choice

Use Mathematical Models Involving Linear Inequalities
-The equation that represents the proper traffic control and emergency vehicle response availability in a small city is 2P + 3F ≤ 23, where P is the number of police cars on active duty and F is the number of fire trucks that have left the firehouse in response to a call. In order to comply with staffing limitations, the equation 2P + F ≤ 17 is appropriate. The number of police cars on active duty and the number of fire trucks that have left the firehouse in response to a call cannot be negative, so P ≥ 0 and F ≥ 0. Graph the regions satisfying all the availability and staffing requirements, using the horizontal axis for P and the vertical axis for F. If 3 police cars are on active duty and 6 fire trucks have left the firehouse in response to a call, are all of the requirements satisfied?

• A) No
• B) Yes
• C) No
• D) Yes

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Definitions:

Firm

A business organization, such as a corporation or partnership, which sells goods or services in exchange for money.

Producer Surplus

The difference between the amount producers are willing to accept for a good or service versus what they actually receive, usually a measure of profit.

Market Price

The price at which a service or asset is presently traded in a given market.

Full Cost

Full cost involves calculating the total cost of production, including both fixed and variable costs, to assess the overall expenses incurred by a business.