Asha was running a business of producing and selling pickles, murabbas and papad etc. She was earning a good p

Question 21 of 26

Q. Asha was running a business of producing and selling pickles, murabbas and papad etc. She was earning a good profit for the last many years. Now, she wanted to add some new products in her product line. Seeing the growing demand of millets, she decided to add some millet products. After doing a lot of market research, she found out that the demand for millet noodles, pasta and ready to eat millet cereals was increasing day-by-day. To give a different taste and to have uniqueness in her products, she prepared a new tasty herb based sauce for cooking these products and decided to launch this along with millet products in the market. For this Asha hired 10 additional women workers specially trained for the same. However, despite adding more workers, to her surprise, production was not upto the mark. Concerned about this and to ensure that the activities were performed as per the plans, and that the resources were being used effectively and efficiently for the achievement of predetermined goals, Asha appointed a supervisor Nabita. Nabita monitored the activities and discovered that two of the newly hired workers were spending their whole day gossiping and distracting the other workers. As a result the production was low.

(i) Identify and state the function of management discussed above.

(ii) State any five points of importance of the function identified in

(i) above.

Lakshadweep CbseCBSE Class XII Board 2025Subjective· 6mImportance★★★★★

81% · 21/26 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

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 $|(3x+1)-7| = 3|x-2| < \epsilon$ . …

Start your 14-day free trial to unlock the full solution →

The case describes the Controlling function of management, which ensures activities align with plans and resources are used efficiently, leading to better goal achievement, resource utilization, and employee discipline.

The scenario presented in the case study highlights a fundamental aspect of management: ensuring that what is planned actually happens, and if not, understanding why and taking corrective action. This isn't just about finding fault; it's about learning, adapting, and continuously improving to achieve the organisation's objectives. Without this crucial function, even the best plans can fail, and resources can be wasted.

Let's break down Asha's situation to identify the specific management function at play and understand its significance.

1. Identifying the Management Function

The case describes Asha's concern when production was "not upto the mark" despite adding workers. Her subsequent actions are key:

She wanted to "ensure that the activities were performed as per the plans".
She aimed to ensure "resources were being used effectively and efficiently for the achievement of predetermined goals".
She "appointed a supervisor Nabita" to "monitor the activities".
Nabita "discovered that two of the newly hired workers were spending their whole day gossiping and distracting the other workers. As a result the production was low."

These actions directly correspond to the Controlling function of management.

Important

Controlling is the process of comparing actual performance with the planned performance, identifying deviations, and taking corrective actions to ensure that activities are performed according to plans and organisational goals are achieved.

Here's why it's Controlling:

Setting Standards: Implicitly, Asha had a standard for production (what was "upto the mark").
Measuring Actual Performance: Nabita "monitored the activities" to see what was actually happening.
Comparing Actual with Standards: Nabita's discovery that production was low indicates a comparison between actual output and expected output.
Analyzing Deviations: Nabita identified the specific reason for low production – gossiping workers.
Taking Corrective Action: While not explicitly stated that Nabita took action, the identification of the problem is the first step towards corrective action, which is the essence of controlling.

Therefore, the function of management discussed is Controlling.

2. Importance of the Controlling Function

The controlling function is vital for any organisation's success. Here are five key points highlighting its importance:

Accomplishing Organisational Goals: Controlling ensures that all activities are performed in accordance with the plans. By continuously monitoring performance and taking corrective actions, it guides the organisation towards its predetermined goals, preventing deviations that could lead to failure. In Asha's case, controlling would help her achieve her production targets for millet products. …

Start your 14-day free trial to unlock the full solution →

←Previous questionQ5 — Umang was working as a 'Production Manager' at 'LG Papers Ltd.' The co…→Next questionQ7 — Sameer is a wholesaler, who deals in cricket equipment. He collects cr…

1. Identifying the Management Function

2. Importance of the Controlling Function

🎓Unlock everything free for 14 days

Unlock everything free for 14 days