All practice questions

The table below presents operating and compliance metrics for seven municipal water treatment plants during 2025:

Match each statement on the left with its correct boolean evaluation outcome and quantitative justification on the right.

An earth-observation satellite payload operator allocates integer numbers of channels to two operational payload modes: High-Resolution Imaging ($I$) and Atmospheric Sounding ($S$). Operational parameters and resource bounds are specified as follows:

- Bandwidth: Each imaging channel requires $15\text{ MHz}$ and each sounding channel requires $10\text{ MHz}$. Total available payload bandwidth is at most $210\text{ MHz}$.
- Power: Each imaging channel consumes $40\text{ W}$ and each sounding channel consumes $15\text{ W}$. Total available power budget is at most $440\text{ W}$.
- Mission Minimums: The satellite must operate at least $2$ imaging channels ($I \ge 2$) and at least $4$ sounding channels ($S \ge 4$).
- Buffer Constraint: The number of sounding channels cannot exceed twice the number of imaging channels ($S \le 2I$).

Match each payload optimization target on the left with its corresponding integer channel count on the right.

A municipal water treatment facility operates four filtration basins (Basin A, Basin B, Basin C, and Basin D). Each basin receives raw water at a specified intake rate and operates at a given recovery percentage (the percent of raw water converted to purified water). Match each filtration basin on the left to its corresponding purified water output rate in thousands of gallons per hour (kgal/hr) on the right.

A regional energy commission classifies proposed energy generation projects into four regulatory permitting tiers based on two quantitative metrics: Peak Capacity (in megawatts, $\text{MW}$) and Sanctuary Proximity (distance in kilometers, $\text{km}$, from a protected wildlife reserve).

The classification criteria are specified as follows:
- Tier 1 (Comprehensive Review): Peak Capacity $> 50\text{ MW}$ AND Sanctuary Proximity $< 10\text{ km}$
- Tier 2 (Grid Impact Priority): Peak Capacity $> 50\text{ MW}$ AND Sanctuary Proximity $\ge 10\text{ km}$
- Tier 3 (Environmental Mitigation Priority): Peak Capacity $\le 50\text{ MW}$ AND Sanctuary Proximity $< 10\text{ km}$
- Tier 4 (Fast-Track Permitting): Peak Capacity $\le 50\text{ MW}$ AND Sanctuary Proximity $\ge 10\text{ km}$

Based on the rules provided above, match each project proposal to its designated regulatory permitting tier.

A commercial bakery operates three distinct production units—Unit X, Unit Y, and Unit Z—to fulfill daily shipments of bread loaves:

- Unit X produces $150$ loaves per hour, with $4\%$ discarded due to minor defects.
- Unit Y produces $200$ loaves per hour, with $5\%$ discarded due to minor defects.
- Unit Z produces $250$ loaves per hour, with $2\%$ discarded due to minor defects.

Match each production unit on the left with its corresponding net yield of non-defective loaves produced during an $8$-hour shift on the right.

A museum conservation board classifies historical artifacts into three management streams based on two parameters: Material Sensitivity (High or Moderate) and Structural Fragility Index (a numerical score from $1$ to $100$). The classification rules are defined as follows:

- Track Y (Long-Term Preservation): Assigned if an artifact has High Material Sensitivity AND a Structural Fragility Index score of at least $70$.
- Track X (Immediate Stabilization): Assigned if an artifact meets EXACTLY ONE of the two conditions (either High Material Sensitivity OR a Structural Fragility Index score of at least $70$, but not both).
- Routine Storage: Assigned if an artifact meets NEITHER condition (Moderate Material Sensitivity AND a Structural Fragility Index score below $70$).

Match each of the following three artifacts to its correct management stream.

A regional logistics operator manages cargo transit on a river corridor using two types of vessels: Express Barges ($E$) and Heavy-Haul Barges ($H$). Weekly operational constraints are defined as follows:

- Fuel Allowance: Each Express Barge consumes $8$ metric tons of fuel per trip, and each Heavy-Haul Barge consumes $12$ metric tons. Total weekly fuel consumption cannot exceed $144$ metric tons.
- Crew Availability: Each Express Barge requires $3$ crew shifts, and each Heavy-Haul Barge requires $2$ crew shifts. Total available crew shifts per week cannot exceed $30$.
- Service Minimum: The operator must deploy at least $2$ Heavy-Haul Barges ($H \ge 2$) per week to maintain baseline commercial obligations.
- Profit Structure: Each Express Barge generates a net profit of $\$5,000$, and each Heavy-Haul Barge generates a net profit of $\$6,000$.

Match each operational metric on the left with its correct optimal value under the profit-maximizing schedule of integer barge deployments.

A venture capital firm classifies its portfolio companies into four strategic management categories based on two quarterly performance metrics: Burn Multiple ($B$) and Customer Retention Rate ($R$).

Classification Criteria:
- Category 1 (Prime Growth): $B \le 1.5$ and $R \ge 85\%$
- Category 2 (Capital Efficient): $B \le 1.5$ and $R < 85\%$
- Category 3 (Expansion Focused): $B > 1.5$ and $R \ge 85\%$
- Category 4 (High Risk): $B > 1.5$ and $R < 85\%$

Match each portfolio company to its corresponding strategic management category.

A municipal transit agency is installing two types of electric vehicle (EV) charging stations at a new central station: Level 2 Chargers ($L$) and Level 3 Fast Chargers ($D$). Each Level 2 charger costs $\$4,000$ to install and draws $10\text{ kW}$ of grid power. Each Level 3 charger costs $\$15,000$ to install and draws $50\text{ kW}$ of grid power. The agency has a total installation budget of $\$100,000$ and a maximum available grid power allocation of $320\text{ kW}$. To meet minimum service grant requirements, the hub must install at least 5 Level 2 chargers ($L \ge 5$) and at least 3 Level 3 chargers ($D \ge 3$). Each Level 2 charger can serve up to 8 sessions per day, and each Level 3 charger can serve up to 30 sessions per day. Match each operational optimization metric on the left with its corresponding correct value on the right that maximizes the total daily charging sessions served by the hub.

A printing company produces two types of customized marketing materials: Standard brochures ($S$) and Premium brochures ($P$). Each Standard brochure requires $2$ minutes of printing time and $1$ minute of binding time. Each Premium brochure requires $3$ minutes of printing time and $3$ minutes of binding time. The production facility has a maximum daily capacity of $240$ minutes for printing and $180$ minutes for binding. Due to a recurring client agreement, the facility must produce at least $20$ Standard brochures per day. The profit is $\$4$ per Standard brochure and $\$9$ per Premium brochure. Match each optimization variable or outcome on the left with its correct value on the right that maximizes daily total profit while satisfying all operational constraints.

A regional emergency health network deploys two types of mobile medical units for event coverage: Rapid Response Units ($R$) and Heavy Support Units ($H$).

The deployment is governed by the following staffing and operational constraints:
- Each Rapid Response Unit ($R$) requires $1$ paramedic and $2$ EMTs.
- Each Heavy Support Unit ($H$) requires $3$ paramedics and $1$ EMT.
- On any given shift, a maximum of $21$ paramedics and $22$ EMTs are available.
- Operational policy mandates deploying at least $3$ Rapid Response Units ($R \ge 3$) and at least $2$ Heavy Support Units ($H \ge 2$).

Each Rapid Response Unit can treat $10$ patients per hour, and each Heavy Support Unit can treat $15$ patients per hour.

Match each operational metric on the left to its corresponding optimal value on the right that maximizes total patient treatment capacity per hour.