Question

The cost and revenue functions of a product are given by C(x) = 20 x + 4000 and R(x) = 60x + 2000, respectively, where x is the number of items produced and sold. How many items must be sold to realise some profit?​

Answer 1

Answer:

The goods should be sold more than 50 in number to get some gain.

Step-by-step explanation:

Given :

Cost = C(x) = 20x + 4000

Revenue functions = R(x) = 60x + 2000

x = number of items produced and sold

To find :

Number of products to be sold to get some gain

Solution :

• Cost → C(x) = 20x + 4000
• Revenue → R(x) = 60x + 2000

$\boxed{\sf{Profit = Revenue - Cost}}$

Subsitute the data provided in the formula :

$\sf{\longrightarrow}\:Profit = R(x) - C(x) \\ \\ \sf{\longrightarrow}\:Profit = (60x + 2000)-(20x + 4000) \\ \\\sf{\longrightarrow}\:Profit = 60x + 2000-20x-4000 \\ \\\sf{\longrightarrow} \:60x - 20x + 2000 - 4000 \\ \\ \sf{\longrightarrow}\:Profit = 40x - 2000$

$\rule{300}{1.5}$

To get some gain : 40x – 2000 > 0

$\sf{\longrightarrow}\:40x > 2000 \\ \\ \sf{\longrightarrow}\:x > \dfrac{2000}{40} \\ \\\sf{\longrightarrow}\:x > 50$

Goods needed = More than 50

$\therefore$ The goods should be sold more than 50 in number to get some gain.

Answer 2

Given:-

=> profit = Revenue – Cost

=> (60x + 2000) – (20x + 4000)

=> 40x – 2000

To earn some profit,

=>40x – 2000 > 0

⇒ x > 50

.°. the manufacturer must sell more than 50 items to realise some profit.