Industry 4.0 · Quiz 2 · Jan 2025

**1. Recover the linked two-asset data:** The same examination’s Corporate Finance passage supplies expected returns μ₁=0.15, μ₂=0.20, standard deviations σ₁=0.25, σ₂=0.30 and covariance σ₁₂=0.04. Let w be the fraction in Asset 1 and 1−w in Asset 2. **2. Minimize portfolio variance:** Differentiating \(w^2\sigma_1^2+(1-w)^2\sigma_2^2+2w(1-w)\sigma_{12}\) gives \[w_{min}=\frac{\sigma_2^2-\sigma_{12}}{\sigma_1^2+\sigma_2^2-2\sigma_{12}}=\frac{0.09-0.04}{0.0625+0.09-0.08}=0.689655.\] The Asset-2 weight is 0.310345. **3. Calculate the expected return:** \[\mu_p=0.689655(0.15)+0.310345(0.20)=0.16551724\ldots=16.55\%.\] **Answer: B — 16.55%.** **Convention note:** This is a Corporate Finance spillover question. Its missing parent data were recovered from the identical two-asset passage in paper 1830 of this same bundle. A: **Incorrect:** It is below both asset returns and cannot result from the positive minimum-variance weights. B: **Correct:** It matches the weighted return at the minimum-variance weights. C: **Incorrect:** It does not use the minimum-variance weight pair. D: **Incorrect:** It puts too much effective weight on the higher-return asset for the variance-minimizing solution.

**1. Classify incoming inspection:** Checking newly received goods is part of procuring and receiving an order, so it is an ordering cost in this inventory classification. **2. Classify stored-product deterioration:** Obsolescence arises while inventory is held and loses usefulness or value. It belongs to carrying cost. **3. Classify inability to serve customers:** Lost goodwill results from not satisfying demand and belongs to shortage cost. Therefore the matching is 1→b,2→c,3→a. **Answer: A — 1: (b), (2): (c), (3): (a).** A: **Correct:** It correctly matches inspection to ordering, obsolescence to carrying and lost goodwill to shortage. B: **Incorrect:** It incorrectly swaps ordering and carrying for the first two costs. C: **Incorrect:** It incorrectly identifies incoming inspection as a shortage cost.

**1. Define exponential smoothing:** The next forecast combines the latest observed demand Dₜ with the previous forecast Fₜ, giving more weight to recent data when α is larger. **2. State the update:** \[F_{t+1}=\alpha D_t+(1-\alpha)F_t,\quad0\le\alpha\le1.\] Repeated substitution expresses older observations with geometrically decreasing weights, which explains the name exponential smoothing. **Answer: A — Fₜ₊₁=αDₜ+(1−α)Fₜ.** A: **Correct:** It is the weighted latest-observation/previous-forecast recursion that defines simple exponential smoothing. B: **Incorrect:** It expresses a mean adjusted by a lagged error term, not the stated simple exponential-smoothing recursion.

**1. Match the integrated shopping channels:** Ordering online and collecting in a physical showroom links channels in one transaction, making a.1 omni-channel retailing (b.4). Merely operating separate channels would be multi-channel. **2. Match the unplanned extra purchase:** The belt is discovered while searching for trousers and was not the original shopping need. That purchase behavior is impulse buying (b.1), even though the belt may also complement trousers. **3. Match the product relationship:** A phone cover is used with the phone rather than replacing it, so a.3 is a complementary product (b.3). The requested matching is 4,1,3. **Answer: C — a.1 : b.4, a.2:b.1, a.3:b.3.** A: **Incorrect:** It labels the integrated pickup arrangement only multi-channel and misses the impulsive purchasing behavior. B: **Incorrect:** It identifies omni-channel correctly but classifies the behavior in a.2 as only a product relationship. C: **Correct:** It matches the integrated channel transaction, impulse purchase and complementary product respectively.

**1. Identify the referenced framework:** The seven-principle IoT framework covers analog-origin data, ongoing connectivity, real-time operation, a spectrum of insights, immediacy versus depth, moving analysis toward the data source, and greater visibility. **2. Distinguish a principle from an application:** Quality control is an important use of sensor data and automation, but it is not one of the seven named principles in that framework. **3. Select what is not in the list:** Quality Control is therefore the requested exception; the other four options are named principles or close paraphrases. **Answer: B — Quality Control.** **Convention note:** The question uses the specific seven-principle IoT framework associated with HPE, not a claim that all IoT literature uses one universal list. A: **Incorrect:** Big Analog Data is one of the named principles, so do not select it. B: **Correct:** Select this exception: quality control is a potential application, not one of the seven principle names. C: **Incorrect:** Constant connection paraphrases perpetual connectivity, a named principle. D: **Incorrect:** Real-time operation is included in the framework. E: **Incorrect:** A complete spectrum of insights is included in the framework.

**1. Define shortage cost:** A shortage occurs when available stock cannot satisfy demand. Its cost includes lost sales and future business damaged by that failure. **2. Apply that definition:** Lost profit on an undelivered sale is direct shortage loss. Losing goodwill or a customer can also reduce future revenue, making both shortage consequences. **3. Separate returns from shortages:** A customer return generally follows a completed sale and may arise from defects or dissatisfaction. It is not inherently caused by having insufficient stock. **Answer: A, C, D — Loss of customer goodwill; Cost of losing a customer; Loss of profit associated with not delivering the product.** A: **Correct:** An unmet order can harm trust and future business. B: **Incorrect:** Returns are a reverse-logistics or quality consequence unless a specific shortage link is supplied. C: **Correct:** A customer may leave because repeated shortages make service unreliable. D: **Correct:** The margin foregone when a sale cannot be fulfilled is a direct shortage cost.

**1. Identify time-dependent patterns:** A forecasting model looks for systematic structure such as trend, seasonality, cycles and persistence in past observations. **2. Relate variables when relevant:** Explanatory time-series forecasting can also discover relationships between a target and other useful series, for example demand and temperature, and use them to improve prediction. **3. Match the requested tasks:** Identifying patterns and discovering relationships are the two substantive modeling tasks listed. Selecting variables of interest is a preparatory problem-definition activity rather than the intended second task. **Answer: A, C — Identifying pattern; Discovering relationships amongst variables of interest.** **Convention note:** A univariate forecast need not include other explanatory variables. C describes the broader relationship-discovery task used in the course’s forecasting framework. A: **Correct:** Recognizing temporal structure is central to forecasting. B: **Incorrect:** Choosing what to measure is preparatory, rather than the intended pattern/relationship discovery task. C: **Correct:** Finding predictive relationships can support multivariate or explanatory forecasts.

**1. Use the EOQ formula:** \(Q^*=\sqrt{2DS/H}\), where D is annual demand, S is cost per order and H is annual holding cost per unit. **2. Compute estimated and actual quantities:** From the estimated inputs, \(Q_e=\sqrt{2(1000)(50)/10}=\sqrt{10000}=100\). From actual inputs, \(Q_a=\sqrt{2(2000)(25)/20}=\sqrt{5000}=70.710678\). **3. Calculate relative error as a percentage:** \[100\frac{Q_e-Q_a}{Q_a}=100\left(\frac{100}{70.710678}-1\right)=41.421356\ldots.\] Enter 41.42 without the percent sign. **Answer: 41.42.**

**1. Put demand and holding cost on the same time basis:** Monthly demand 1500 becomes D=1500×12=18000 units/year. Annual holding cost per unit is H=0.20×27=5.40 rupees. Ordering cost S=150 rupees/order. **2. Minimize ordering plus holding cost:** For a fixed purchase price and no shortages, \(TC(Q)=DS/Q+HQ/2\). Setting its derivative to zero gives \(Q^*=\sqrt{2DS/H}\). **3. Substitute and simplify:** \[Q^*=\sqrt{\frac{2(18000)(150)}{5.4}}=\sqrt{1000000}=1000\text{ units/order}.\] **Answer: 1000.**

**1. Find annual demand and EOQ:** Demand is 1500×12=18000 units/year. With ordering cost 150 and annual holding cost 0.20×27=5.4, \(Q^*=\sqrt{2(18000)(150)/5.4}=1000\) units. **2. Divide demand by order size:** \[N=D/Q^*=18000/1000=18\text{ orders/year}.\] This assumes the steady-demand EOQ model with replenishment as specified. **Answer: 18.**

**1. Calculate underage and overage costs:** Treat the selling price as p=2 rupees, purchase/production cost as c=1 and end-season salvage value as v=0.5. Underage cost is Cᵤ=p−c=1, while overage cost is Cₒ=c−v=0.5. **2. Apply the newsvendor critical ratio:** \[CR=\frac{C_u}{C_u+C_o}=\frac1{1+0.5}=\frac23=0.666666\ldots.\] Rounding to two decimals gives 0.67. This ratio identifies the demand percentile to stock for, not the quantity directly. **Answer: 0.67.**

**1. Determine the target demand percentile:** With p=2,c=1,v=0.5, the critical ratio is \((p-c)/(p-v)=1/1.5=2/3\). **2. Use the uniform demand CDF:** For demand uniform on [800,1000], \(F(Q)=(Q-800)/200\) inside that interval. The optimal continuous stock satisfies F(Q*)=2/3. **3. Solve:** \[Q^*=800+200(2/3)=933.3333\ldots.\] The continuous newsvendor answer is 933.33 units. If whole diyas must be chosen, comparison of adjacent feasible integers gives 933 units under the continuous-uniform model. **Answer: 933.33.**

**1. Define a dynamic-programming state:** At each stage, the current state must tell us where the traveler is before choosing the next road. Here it is the city at the beginning of that stage. **2. Separate state from action and cost:** Selecting the next city is the action, and distance is the cost accumulated or remaining. A backward value function J(i) stores the minimum remaining distance starting from current city i. **Answer: B — The beginning city in every stages.** **Convention note:** The options call the traveler Ramu, while the passage calls him Govind; this naming typo does not change the state definition. A: **Incorrect:** The next city is chosen by the action rather than being the current state. B: **Correct:** The beginning/current city identifies the state before a stage’s decision. C: **Incorrect:** Distance is a cost value, not the location state in this formulation.

**1. Define the available action:** Given current city i, choose a directly connected successor city j. The feasible action set consists of those successors for which an outgoing road exists. **2. Apply the road restriction:** For example, from City 2 the diagram permits City 5 and explicitly excludes City 6. This is a restriction on feasible actions, not on the definition of the state or distance cost. **Answer: A — The city Ramu should visit next in a stage.** **Convention note:** The traveler-name inconsistency in the options is a typographical error. A: **Correct:** Choosing the next city is exactly the decision available at a stage. B: **Incorrect:** The city at the beginning of the stage is the state. C: **Incorrect:** Distance is the objective’s cost, not an action.