Word problem, equations

Question

You're the Vice President of a company that sells sunglasses. Through some initial data collecting it's determined that for every additional $0.50 profit you make on each sale you lose 80 daily sales. Right now you sell the sunglasses at a $2 profit and sell 1040 pairs daliy. At what profit should you set your sunglasses at? How much profit will this give you daily? (find the amount that will give the most profiit)

Answer 1

Here is the mathematical equation for profit

 

y = (1040 - 80x)(2 + ½x)  //y = profit and x = by how much factor you increase/decrease your profit

 

If you plot the graph for this equation you will see that it peacks right around x = 5.

That means 5(½) + 2 = $4.50

 

Profit = (1040 - 80(5))(2+0.5(5)) = 2880

 

hope this helps

Answer 2

You need to come up with a formula for profit we know the relationship between profit and sales is an inverse relationship the higher profit margin the lower the sales. Profit increases by $.50 sales drop 80 units so

Profit = Profit per unit × units sold

Profit = ($2+$.50X)(1040-80X)

Profit = $2080+$360X-$40X^2

You must maximize this function

The roots are -4 and 13. The max would be midway between the roots at4.5.

When you plug this into your formula you find the profit should be$4.25 per unit which will lead to 680 units sold daily and a daily profit of$2890