March 29, 2017

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Hello! I came across the following two problems that appear easy but I was not able to construct the needed equations.

(1) The profit (in thousand of dollars) on x thousand units of a specialty item is p = 0.6x - 14.5. The cost c of manufactoring x thousand items is given by c = 0.8x + 14.5.

(A) Find an equation that gives the revenue r from selling x thousand items.

The correct equation is r = 1.4x but where did 1.4 come from?
Is 1.4 the slope? If so, how is the slope produced using the given information above?

Someone suggested that profit = revenue - cost and that I should add the two given slopes 0.6 + 0.8 to get 1.4 as the new slope. However, profit = revenue MINUS cost not PLUS cost. Why do I need to add 0.6 and 0.8?

(B) How many items must be sold for the company to break-even?

I understood breaking-even to means when revenue equals cost.

I decided to let p = 0 in the profit equation given above and solve for x.

I got x = 24 but I am so far from the right answer. What did I do wrong?

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