Question

A company has determined that its profit for a product can be described by a linear...

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?

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Answer #1

Answer-

(I)

Consider the profit from the production and sale of 150 units is and the profit from 250 units is.

Need to find the average rate of change of the profit.

The average rate is

Hence, the average rate is.

(ii)

Need to find the equation of the profit function.

To find the equation of the profit function uses the formula.

Use

Hence, the equation of the profit function is.

(iii)-Break even units means, the units produce zero profit.

To find the break-even point set and solve for x.

The units can’t be negative.

Hence, the break even at nearly

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