Question

An owner of an electric bike rental company has determined that if they charge customers Rs x per day to rent a bike, where 50 < x < 200, then number of bikes (n), they rent per day can be shown by linear function n(x) = 2000 - 10x. If they charge Rs. 50 per day or less, they will rent all their bikes. If they charge Rs. 200 or more per day, they will not rent any bike. Based on the above information, answer the following questions. () Total revenue R as a function of x can be represented as (a) 2000x - 10x^2 (b) 2000x + 10x^2 (c) 2000 - 10x (d) 2000 - 5x^2 (ii) If R(x) denote the revenue, then maximum value of R(x) occur when x equals (a) 10 (b) 100 (c) 1000 (d) 50 (iii) At x = 260, the revenue collected by the company is (a) Rs. 10 (b) Rs. 500 (c) Rs. 0 (d) Rs. 1000 (iv) The number of bikes rented per day. if x = 105 is (a) 850 (b) 900 (c) 950 (d) 1000 (v) Maximum revenue collected by company is (a) Rs. 40.000 (b) Rs. 50,000 (c) Rs. 75,000 (d) Rs. 1,00,000​

Answer 1

SOLUTION

CORRECT QUESTION

An owner of an electric bike rental company has determined that if they charge customers Rs. x per day to rent a bike, where 50 ≤ x ≤ 200, then number of bikes (n), they rent per day can be shown by linear function n(x) = 2000 - 10x. If they charge Rs. 50 per day or less, they will rent all their bikes. If they charge Rs. 200 or more per day, they will not rent any bike.

Based on the above information, answer the following questions.

(i) Total revenue R as a function of x can be represented as

(a) 2000x – 10x²

(b) 2000x + 10x²

(c) 2000 – 10x

(d) 2000 – 5x²

(ii) If R(x) denote the revenue, then maximum value of R(x) occur when x equals

(a) 10

(b) 100

(c) 1000

(d) 50

(iii) At x = 260, the revenue collected by the company is

(a) Rs. 10

(b) Rs. 500

(c) Rs. 0

(d) Rs. 1000

(iv) The number of bikes rented per day if x = 105 is

(a) 850

(b) 900

(c) 950

(d) 1000

(v) Maximum revenue collected by company is

(a) Rs. 40.000

(b) Rs. 50,000

(c) Rs. 75,000

(d) Rs. 1,00,000

EVALUATION

Here by the given , the number of bikes (n), they rent per day can be shown by linear function

n(x) = 2000 - 10x

(i) Total revenue function

= R(x)

= x.n(x)

$\sf = x(2000 - 10x)$

$\sf = 2000x - 10 {x}^{2}$

Hence the correct option is (a) 2000x – 10x²

(ii) We have R(x) = 2000x – 10x²

R'(x) = 2000 – 20x

For maximum value of R(x)

R'(x) = 0

⇒ 2000 - 20x = 0

⇒ 20x = 2000

⇒ x = 100

Thus maximum value of R(x) occur when x = 100

Hence the correct option is (b) 100

(iii) Since x = 260 does not lie in the interval 50 ≤ x ≤ 200

So the revenue collected by the company = 0

Hence the correct option is (c) Rs. 0

(iv) When x = 105

The number of bikes rented per day

= 2000 - ( 10 × 105 )

= 2000 - 1050

= 950

Hence the correct option is (c) 950

(v) The maximum value of R(x) occur when x = 100

Hence the Maximum revenue collected by company

$\sf =( 2000 \times 100) -( 10 \times {100}^{2} )$

$\sf = 200000 -100000$

$\sf = 100000$

Hence the correct option is (d) Rs. 1,00,000

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