[Case Based] LED bulbs are energy-efficient because they use

Question 37 (Case Based Questions) LED bulbs are energy-efficient because they use significantly less electricity than traditional bulbs while producing the same amount of light. They convert more energy into light rather than heat, reducing waste. Additionally, their long lifespan means fewer replacements, saving resources and money over time. A company manufactures a new type of energy-efficient LED bulb. The cost of production and the revenue generated by selling x bulbs (in an hour) are modelled as 𝐶(𝑥)=0.5𝑥^2−10𝑥+150" and " 𝑅(𝑥)=−0.3𝑥^2+20𝑥 "respectively, where" 𝐶(𝑥)" and " 𝑅(𝑥)" are both in ₹." To maximize the profit, the company needs to analyze these functions using calculus. Use the given models to answer the following questions:Question 37 (i) Derive the profit function 𝑃(𝑥)Given Cost = 𝐶(𝑥)=0.5𝑥^2−10𝑥+150" " Revenue = 𝑅(𝑥)=−0.3𝑥^2+20𝑥 Let P(𝒙) be the profit Now, Profit = Revenue – Cost P(𝒙) = R(𝒙) – C(𝒙) P(𝑥) = (−0.3𝑥^2+20𝑥)−(0.5𝑥^2−10𝑥+150) P(𝑥) = −0.3𝑥^2+20𝑥−0.5𝑥^2+10𝑥−150 P(𝑥) = (−0.5−0.3) 𝑥^2+20𝑥+10𝑥−150 P(𝒙) = −𝟎.𝟖𝒙^𝟐+𝟑𝟎𝒙−𝟏𝟓𝟎

Question 37 (i) - CBSE Class 12 Sample Paper for 2026 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Davneet Singh

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular