Vikas was the Chief Operating Officer of 'Yalet Ltd.', a company providing advanced software solutions to Indi

Question 26 of 26

Q. Vikas was the Chief Operating Officer of 'Yalet Ltd.', a company providing advanced software solutions to Indian Defence Services. They had been carrying on business successfully for the last twelve years and earning enough profits. But from the last one year, they realised that though the business is getting big orders which are being fulfilled in time, even then the revenues kept on decreasing. Vikas was not able to find out where the problem was. He started keeping a close check on the progress of activities as he could sense that something was wrong. He wanted to take some action before any major damage could be done to the business. Vikas appointed a cyber security expert who monitored the company's processes and found out that the computer operator was deleting the entries from the computers and pocketing the revenues. He was caught and handed over to the police. This created an atmosphere of order and discipline in the organisation and helped in minimising dishonest behaviour on the part of the employees.

(a) Identify the function of management highlighted in the above paragraph.

(b) Explain any four other ways in which this function of management may help the organisation.

Punjab PsebCBSE Class XII Board 2019Subjective· 5mImportance★★★★★

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Concept understanding — Controlling Definition

Controlling Definition — First Encounter

Imagine you're trying to prove that a function is continuous at a point. You've seen the epsilon-delta definition: for every $\epsilon > 0$ , there exists a $\delta > 0$ such that if $|x - c| < \delta$ , then $|f(x) - f(c)| < \epsilon$ . That's the standard definition.

Now think about what you're actually doing when you use this definition to prove continuity. You're given an arbitrary $\epsilon$ — a tolerance on the output — and you must produce a $\delta$ — a window on the input — that controls the output error. The $\delta$ you choose depends on $\epsilon$ , on the function $f$ , and on the point $c$ . The core idea: you control the input to control the output.

That's the intuition behind the term "controlling definition." It's a definition that tells you: to achieve a desired precision in the output, you must restrict the input within some range. The definition itself gives you the control — the $\delta$ — as a function of the desired precision $\epsilon$ .

The Precise Statement

A controlling definition is a definition of a limit (or continuity, or derivative) that explicitly quantifies the relationship between an output tolerance and an input restriction. For the limit $\lim_{x \to c} f(x) = L$ , the controlling definition is:

\lim_{x \to c} f(x) = L \iff \forall \epsilon > 0, \ \exists \delta > 0 \ \text{such that} \ 0 < |x - c| < \delta \implies |f(x) - L| < \epsilon

The word "controlling" highlights that $\delta$ is chosen after $\epsilon$ is given — you control the input window $\delta$ to force the output error below $\epsilon$ . The $\delta$ is not arbitrary; it must be found (or shown to exist) for every possible $\epsilon$ .

Why "Controlling" Matters

This phrasing is most common in analysis textbooks when contrasting with other equivalent definitions. For example, the "sequential definition" of a limit says: if every sequence $x_n \to c$ (with $x_n \neq c$ ) has $f(x_n) \to L$ , then the limit exists. That definition doesn't give you a direct control mechanism — it's about checking sequences.

The controlling definition is the one you actually use in proofs. It's constructive: you pick $\delta$ as a function of $\epsilon$ , often by solving inequalities. For instance, to prove $\lim_{x \to 2} (3x+1) = 7$ , you set $\delta = \epsilon/3$ . That's the control: if $|x-2| < \epsilon/3$ , then $|(3x+1)-7| = 3|x-2| < \epsilon$ . …

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The function highlighted is Controlling — Vikas monitored performance, detected deviation (missing revenues), identified the cause (fraud), and took corrective action (appointing an expert, catching the culprit). Controlling also helps by ensuring goal achievement, efficient resource use, maintaining standards, and facilitating coordination across the organisation.

The scenario describes a classic application of the controlling function of management. Controlling is the process of monitoring actual performance against planned standards, identifying deviations, diagnosing their causes, and taking corrective action to bring performance back on track.

Why does controlling matter? Every organisation sets goals and makes plans, but execution rarely goes perfectly. Markets shift, people make mistakes, systems fail, and sometimes — as in Vikas's case — deliberate fraud occurs. Without a mechanism to check whether things are proceeding as intended, even a profitable business can silently bleed resources. Controlling acts as the organisation's early-warning system and course-correction mechanism.

In Yalet Ltd., the symptom was clear: revenues were falling despite timely order fulfilment. Vikas sensed something was wrong (the essence of controlling is vigilance), investigated systematically, discovered the root cause (embezzlement by the computer operator), and took corrective action (legal action, restoring discipline). This is controlling in action.

(a) Function of Management Highlighted

The function of management highlighted in the paragraph is Controlling.

Vikas observed a deviation (decreasing revenues despite business growth), monitored activities closely, identified the cause (fraudulent deletion of entries), and took corrective measures (appointing a cyber expert, catching the operator, restoring order). This entire sequence — measure, compare, diagnose, correct — is the controlling cycle.

(b) Four Other Ways Controlling Helps the Organisation

Beyond catching fraud, controlling serves several vital roles in any organisation:

1. Ensures Achievement of Organisational Goals

Controlling compares actual performance with predetermined standards and objectives. If sales targets, production quotas, or quality benchmarks are not being met, controlling flags the gap early. Managers can then reallocate resources, revise strategies, or provide additional training to employees. Without this feedback loop, an organisation might drift off course for months before realising it has missed its targets.

Tip

Think of controlling as a GPS for management: it tells you not just where you are, but whether you're still heading toward your destination.

2. Facilitates Efficient Use of Resources

By monitoring resource consumption — materials, labour hours, machine time, budgets — controlling identifies waste, inefficiency, and cost overruns. For instance, variance analysis in standard costing reveals whether more raw material was used than planned, or whether labour took longer than expected. Managers can then investigate: Was it poor training? Defective materials? Machine breakdown? Corrective action (retraining, supplier change, maintenance) follows, ensuring resources are used optimally.

3. Maintains and Improves Standards …

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(a) Function of Management Highlighted

(b) Four Other Ways Controlling Helps the Organisation

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