(a) A company has determined that its profit for a product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from 250 units is $895. (i) What is the average rate of change of the profit for this product when between 150 and 250 units are sold? (ii) Write the equation of the profit function for this product. (iii) How many units give break-even for this product?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) A company has determined that its profit for a product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from 250 units is $895.

(i) What is the average rate of change of the profit for this product when between 150 and 250 units are sold?

(ii) Write the equation of the profit function for this product.

(iii) How many units give break-even for this product?

(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 − 4q 2 where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass

(i) Write an equation giving profit as a function of the number of lightweight compasses produced.

(ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?

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