An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function [tex]p(x) = -x^2 + 350x - 6600[/tex], where [tex]p(x)[/tex] is the profit in thousand Rupees and [tex]x[/tex] is the number of automobiles made and sold. Answer the following questions based on this model:

(i) What is the profit/loss when no cars are produced?

(ii) What is the break-even point? (Zero profit point is called break-even).

(iii) What is the profit/loss if 400 cars are produced?

Question

College

We appreciate your visit to An automobile manufacturer can produce up to 300 cars per day The profit made from the sale of these vehicles can be modeled by the. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Answer :

AFOKE88 AFOKE88 · Answer 1 · 2024-09-29T22:07:46-04:00

i) The profit/loss when no cars are produced is a loss of 6600 Rupees.

II) The break even point is at 20 cars

III) The profit/loss if 400 cars are produced is; a loss of 13400Rupees.

(i) When no cars are produced, x = 0.

Thus, plugging this value into the function p(x) = -x² + 350x - 6600, we have;

p(0) = -0² + 350(0) - 6600 = -6600.

Therefore, the profit/loss when no cars are produced is a loss of 6600 thousand Rupees.

(ii) The break-even point is the point at which the profit is zero, i.e., p(x) = 0. Setting p(x) = 0 and solving for x, we find that;

-x² + 350x - 6600 = 0

x = 20

Therefore, the break-even point is x = 20 cars. T

(iii) If 400 cars are produced, the profit can be found by plugging this value into the function p(x) = -x² + 350x - 6600.

We find that p(400) = -400² + 350(400) - 6600

= -160000 + 140000 + 6600 = -13400. Therefore, the profit/loss if 400 cars are produced is a loss of 13400 Rupees.

Read more about Profit Functions at; https://brainly.com/question/25638609

#SPJ1