Please solve all the questions below from supply chain analytics subject and give me correct answer options$-$

Q$1)$Which of the following statements is$/$are correct?

The capability of fulfilling customer demand from available inventory is one of the primary measures of supply chain$$s responsiveness.

The cost of overstocking is the margin lost by a firm for each lost sale because there is no inventory on hand.

The cost of understocking is the loss incurred by a firm for each unsold unit at the end of the selling season.

All of the above

Q$2)$

Statement I: A supply chain must achieve a balance between the level of availability and the cost of inventory.

Statement II: The optimal level of product availability is one that maximizes supply chain profits.

Only Statement I is correct.

Only Statement II is correct.

Both the statements are correct.

Both the statements are incorrect.

Q$3)$

Consider the following table:

Demand $($in units$)151617181920212223242526272829$

Probability $0\mathrm{.}010\mathrm{.}020\mathrm{.}030\mathrm{.}050\mathrm{.}070\mathrm{.}10\mathrm{.}120\mathrm{.}120\mathrm{.}110\mathrm{.}090\mathrm{.}090\mathrm{.}080\mathrm{.}060\mathrm{.}040\mathrm{.}01$

Cost per unit: $25$

Selling price per unit: $75$

Scrap value per unit: $12$

Handling cost of handling scrap: $5$

What is the expected profit if the stock is $20$ units, considering the costs of understocking and overstocking?

$935\mathrm{.}72$

$1027\mathrm{.}24$

$1004\mathrm{.}44$

$973\mathrm{.}48$

Q$4)$

XYZ Corporation is contemplating investing in a new warehouse automation system to streamline its supply chain operations. The initial cost of the automation system is $$300,000.$ The system is projected to generate annual savings of $80,000$ for the next $7$ years. Given a discount rate of $10\%,$ which of the following is the net present value $($NPV$)($nearest value$)$ to make the decision:

$80,000$

$90,000$

$1,00,000$

$1,10,000$

Q$5)$

Match the following type of analytics to the suitable example

Type Example

a$.$ Descriptive i$.$ Demand Forecasting

b$.$ Predictive ii$.$ Supply Chain Optimization

c$.$ Prescriptive iii. Inventory Reports

a$-($i$),$ b$-($ii$),$ c$-($iii$)$

a$-($iii$),$ b$-($i$),$ c$-($ii$)$

a$-($iii$),$ b$-($ii$),$ c$-($i$)$

a$-($ii$),$ b$-($iii$),$ c$-($i$)$

Q$6)$

Statement I: Prescriptive analytics uses statistical models and forecasts to ask: $$What could happen?$$

Statement II: Predictive analytics uses optimization and embedded decision rules and simulation to ask: $$What should we do$?$

Only Statement I is correct.

Only Statement II is correct.

Both the statements are correct.

Both the statements are incorrect.

Q$7)$

Which of the following statements is correct regarding predictive analytics?

It is important to increase reliability of predictive modelling so as to reduce forecasting errors leading to various issues in supply chain like overstocking, understocking, bullwhip effect etc.

It uses historical data and various algorithms to predict outcomes of different what$-$if scenarios.

It is even more so useful now that we have huge amount of data available.

All of the above

Q$8)$

Which of the following is not one of the common uses of predictive analytics?

Fraud detection

Optimizing marketing campaigns

Defining consumer characteristics

Reducing risk

Q$9)$

Which of the following is the correct sequence on how to start using predictive analytics?

problem identification$->$ data collection and preparation$->$ model building$->$ team approach

team approach$->$ problem identification$->$ data collection and preparation$->$ model building

problem identification$->$ model building$->$ data collection and preparation$->$ team approach

problem identification$->$ data collection and preparation$->$ team approach$->$ model building

Q$10)$

In a multiplicative binomial representation of uncertainty, the probability of an increase in demand D by a factor of $$u$($u$>1)$ is $$p$($p$<1),$ and the decrease in demand by a factor of $$d$($d$<1)$ is $1-$p$$ after each period. Which of the following is true about the maximum possible demand after $3$ periods?

The probability for maximum possible demand will be greater than p

The probability for maximum possible demand will be less than p

The probability for maximum possible demand will be equal to p

It can take any value