I came across the followingquestion that appears easy. I was not able to constru

Question

I came across the followingquestion that appears easy. I was not able to construct the neededequation.

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

(A) Findan equation that gives the revenue r from selling x thousanditems.

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 informationabove?

Also does profit = revenue - cost? I was toldto add the two given slopes 0.6 + 0.8 to produce 1.4 asthe new slope. However, profit = revenue MINUS cost not PLUS cost. Why do I need to add0.6 and 0.8?

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

I understood breaking-even to mean when revenue equals cost. Is this right?

In that case, I decided to let p = 0 in the profit equation givenabove and solve for x.

I got x = 24 but it's not the right answer. What did I dowrong?

I came across the followingquestion that appears easy. I was not able to construct the neededequation.

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

(A) Findan equation that gives the revenue r from selling x thousanditems.

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 informationabove?

Also does profit = revenue - cost? I was toldto add the two given slopes 0.6 + 0.8 to produce 1.4 asthe new slope. However, profit = revenue MINUS cost not PLUS cost. Why do I need to add0.6 and 0.8?

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

I understood breaking-even to mean when revenue equals cost. Is this right?

In that case, I decided to let p = 0 in the profit equation givenabove and solve for x.

I got x = 24 but it's not the right answer. What did I dowrong?

Explanation / Answer

profit + cost=  revenue (you are taking in money to cover costplus a little extra for profit) so you add ( 0.6x -14.5)+(0.8x + 14.5)= 1.4x=r and 1.4 is the slope
breaking-even to mean whenrevenue equals cost so you need to set them equal to eachother (you can make 0 profit andnot break even) 1.4x=0.8x +14.5 .6x=14.5 x=24 1/6 thousandunits

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