**Case Study-II.**

A manufacturing company manufactures toys; the company observed the following costs at different production levels:

| Number of toys manufactured | Cost of raw material (₹) | Cost of Production Supply (₹) | Cost of freight (₹) | Property tax (₹) | Salaries (₹

Question

**Case Study-II.**

A manufacturing company manufactures toys; the company observed the following costs at different production levels:

| Number of toys manufactured | Cost of raw material (₹) | Cost of Production Supply (₹) | Cost of freight (₹) | Property tax (₹) | Salaries (₹) |
|---|---|---|---|---|---|
| 100 | 800 | 2000 | 1000 | 5000 | 20000 |
| 150 | 1200 | 3000 | 1500 | 5000 | 20000 |
| 200 | 1600 | 4000 | 2000 | 5000 | 20000 |
| 250 | 2000 | 5000 | 2500 | 5000 | 20000 |
| 300 | 2400 | 6000 | 3000 | 5000 | 20000 |

Based on the above information, answer the following.

1. Which of the following is the fixed cost
   (i) Number of toys manufactured
   (ii) Cost of raw material
   (iii) Cost of production supply
   (iv) Salaries
2. Total cost $C(x)$ of toys for '$x$' units of production is
   (i) $C(x) = 8x^2 + 30x + 25000$
   (ii) $C(x) = 8x^2 + 30x + 20000$
   (iii) $C(x) = 38x + 25000$
   (iv) $C(x) = 28x + 25000$
3. If the company observes the price '$p$' per unit of item sold $p = 5000 - 10x$, where the '$x$' is the number of units sold, then the revenue function $R(x)$ is given by,
   (i) $R(x) = 5000x - 10x^2$
   (ii) $R(p) = 5000p - 10p^2$
   (iii) $R(x) = 5000 - 10x^2$
   (iv) $R(p) = 5000 - 10p^2$
4. The Marginal revenue (MR) of the company is given by
   (i) $5000 - 20x$
   (ii) $5000 - 20p$
   (iii) $-20x$
   (iv) $-20p$
5. If the profit function $P(x) = R(x) - C(x)$, then it is given by
   (i) $-18x^2 + 4970x - 25000$
   (ii) $-10x^2 + 4962x - 20000$
   (iii) $10x^2 + 4962x - 25000$
   (iv) $-10x^2 + 4962x - 25000$

Accepted Answer

> [!TLDR]
> Salaries (₹20,000, unchanged at every output) are the fixed cost among the options; the variable costs give $C(x)=38x+25000$, revenue $R(x)=5000x-10x^2$, marginal revenue $5000-20x$, and profit $P(x)=-10x^2+4962x-25000$.

> [!FORMULA]
> A fixed cost stays constant as output changes; total cost $C(x)=(	ext{variable cost per unit})\,x+(	ext{fixed cost})$; revenue $R=p\cdot x$; marginal revenue $	ext{MR}=R'(x)$; profit $P(x)=R(x)-C(x)$.

From the table, the costs of raw material, production supply and freight all rise with output, while property tax (₹5000) and salaries (₹20000) stay the same at every production level.

1. Among the listed options, **salaries** are the same (₹20,000) at every output level, so salaries are the **fixed cost** → option **(iv)**. …

Number of toys manufactured	Cost of raw material (₹)	Cost of Production Supply (₹)	Cost of freight (₹)	Property tax (₹)	Salaries (₹)
100	800	2000	1000	5000	20000
150	1200	3000	1500	5000	20000
200	1600	4000	2000	5000	20000
250	2000	5000	2500	5000	20000
300	2400	6000	3000	5000	20000

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