A manufacturer of electric kettles faces the following economic data: Demand…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A manufacturer of electric kettles faces the following economic data:
Demand (price–quantity) relation: p=1200−5x,
Total cost function: C(x)=100000+200x+0.2x2,
Indirect tax: An excise duty of Rs. 50 is payable per kettle produced.
Here x (a positive integer) is the number of kettles produced and sold and p (in rupees) is the selling price per kettle.
Respond to the questions below.
(i) Formulate the profit function P(x) after including the tax liability.
(ii) Determine the production level x and the corresponding selling price p that maximise the manufacturer’s profit.
(iii) Calculate the maximum profit that the manufacturer can earn under the given conditions.
(iv) Confirm, using an appropriate derivative test, that the value of x found in part (ii) gives a maximum profit.