A firm maximizes profit Z = 40x + 30y subject to 2x + y ≤ 100 and x, y ≥ 0. At the corner point (50, 0), the profit is:
Operations Research
Question · Medium
Where does this beam break first?
Short
In an M/M/1 queuing system, arrival rate λ = 8 customers/hour and service rate μ = 10 customers/hour. The average number in the system L is:
Annual demand D = 12,000 units, ordering cost S = 100 SAR/order, and holding cost H = 2 SAR/unit/year. The economic order quantity (EOQ) is:
Question · Hard
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In decision analysis, the expected monetary value (EMV) of a gamble with 60% chance of +10,000 SAR and 40% chance of −4,000 SAR is:
A shadow price (dual value) in LP indicates:
Fishbone diagram, x-rayed
In an assignment problem with n workers and n jobs, the Hungarian method finds:
A PERT activity has optimistic time 4 days, most likely 6 days, and pessimistic 10 days. The expected duration te is:
For M/M/1 with λ = 9/hr and μ = 12/hr, average time in system W (hours) is:
The simplex method iterates by:
OSHA noise limits
The 5th percentile female stature is most relevant when designing:
Ergonomics
NIOSH recommended weight limit (RWL) decreases when horizontal distance of the load from the body:
Question · Easy
Recommended illuminance on detailed assembly tasks is generally:
Cumulative trauma disorders (CTDs) in industrial work are most associated with:
Methods-Time Measurement (MTM) is used to:
Work Design
If workplace noise level is 90 dBA and permissible exposure without hearing protection is 85 dBA, engineering controls should aim to:
A worker's resting metabolic rate is 1.2 kcal/min. At 3 METs, estimated energy expenditure is:
The primary purpose of a Job Safety Analysis (JSA) is to:
Recommended work-rest schedule for hot industrial environments in Saudi Arabia should consider:
A line has 5 stations with task times 40, 50, 60, 50, and 40 seconds. The minimum number of workstations for a cycle time of 60 s is:
Production Systems
Takt time is calculated as:
A bottleneck in a production line is the station with:
Overall Equipment Effectiveness (OEE) combines:
Kanban cards in a pull system signal:
MRP (Material Requirements Planning) uses:
A cellular manufacturing layout groups machines by:
Poka-yoke (mistake-proofing) examples include:
Manufacturing lead time typically includes:
For an X-bar chart with subgroup size n = 4, σ known, center line is process mean μ. Control limits are at μ ±:
Quality Engineering
Process capability index Cp = (USL − LSL)/(6σ) measures:
The DMAIC framework in Six Sigma stands for Define, Measure, Analyze, Improve, and:
A fishbone (Ishikawa) diagram is used to:
If process mean μ = 50, target = 50, USL = 56, LSL = 44, σ = 2, Cpk = min[(USL−μ)/3σ, (μ−LSL)/3σ] is:
Gauge R&R studies measure:
An R chart uses subgroup range R̄ = 4.2 with n = 5 and D4 = 2.114. The upper control limit UCL_R ≈
The Taguchi loss function views quality cost as:
Failure Mode and Effects Analysis (FMEA) prioritizes risks using:
Present worth of 5,000 SAR received in 3 years at i = 8% annually is closest to:
Engineering Economy
An investment of 10,000 SAR returns 12,000 SAR in one year. The annual rate of return is:
Benefit-cost ratio B/C > 1 for a public project indicates:
Straight-line depreciation of an asset costing 100,000 SAR with salvage 10,000 SAR over 5 years gives annual depreciation:
Annual worth (AW) of a project is equivalent to:
Payback period ignores:
If PW of benefits = 800,000 SAR and PW of costs = 500,000 SAR, B/C ratio is:
Capitalized cost (perpetual service) formula uses:
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