A student posted this problem back in September, 2020. I'll bet they'll get a
big laugh when they are notified that 4 1/2 years later, they finally got an
answer, now that they're no longer in school. 

Notice the date:  168304 (2020-10-26 21:49:28)

The date disappears when we answer. 

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

Let the function be

y = mx + b, where y is profit, and x is the number of units.

The profit from the production and sale of 150 units is $455, 

When x = 150, y = 455.  We substitute in y = mx+b.

455 = m(150) + b or

150m + b = 455.

and the profit from 250 units is $895.

When x = 250, y = 895.  We substitute in y = mx+b.

895 = m(250) + b or

250m + b = 895.

Solve the system of equations:



Subtract the two equations term by term and the b's cancel.






So the equation is 



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

That is the slope or 4.4 more dollars per unit sold.

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

 although you can write using P for y and U for x.



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

That's when the profit is 0







 

about 47.6 units give break-even for this product.

Sorry it took so 4.5 years to get an answer, but back then there were too
many problems posted and not enough tutors.  Nowadays there are more tutors
than posts.

Edwin