Question

Your firm is considering adding a product line. The accounting department is determined that the cost function for this product will be c(x) = 145x + 2940 and the revenue function will be R(x) = 175x where x is the number of units sold. Additionally the sales department has determined that you reasonably can expect to sell around 121 units. You must decide whether to go ahead with the new product line.

Find the break even quantity__________
Find the Profit function: P(x) = _________

Answer 1

break-even point is when the sales match your costs, so if you spent $100 on the products and you sell $100 at some point, that's your break-even point, your cost are covered, well no profits but no losses either. Well, that happens when obviously enough R(x) = C(x)

`\stackrel{R(x)}{175x}~~ = ~~\stackrel{C(x)}{145x+2940}\implies 30x=2940\implies x=\cfrac{2940}{30}\implies \stackrel{ units~sold }{x=98}`

profit is surplus from your costs, so, so long your sales exceed your costs, whatever is over the costs, is your Profit, so not so oddly enough Profits is the difference from revenue and costs, namely R(x) - C(x).

`P(x)=\stackrel{R(x)}{175x}~~ - ~~\stackrel{C(x)}{(145x+2940)}\implies P(x)=30x-2940`