MobiStar is a mobile services company that sells 800 Obile services company that sells 800 phones each week when it charges $80 per phone. It sells 40 more phones per week for each $2 decrease in price. The company's revenue is the product of the number of phones sold and the price of each phone. What price should the company charge to maximize its revenue?
+23245 Let us say that each week, the company decreases the cost by $2.00 and the number sold will increase by 40.
Let x = number of weeks
Then the number sold = 800 + 40x
and the cost per phone = $80.00 - $2.00x
Revenue = (800 + 40x)(80 - 2x)
To graph this, rewrite as: y = (800 + 40x)(80 - 2x)
Multiply out: y = 64000 + 1600x - 80x2 (This is a parabola)
Find the vertex: y - 64000 = -80x2 + 1600x
y - 64000 = -80(x2 - 20x)
Complete the square: y - 64000 - 8000 = -80(x2 - 20x + 100)
y - 72000 = -80(x - 10)2
So, after 10 weeks, the number sold will be 800 + 40(10) = 1200
and the cost per phone will be $80.00 - $2.00(10) = $60.00.
