A candlemaker prices one set of scented candles at $10 and sells an average of 200 sets each week. He finds that when he reduces the price by $1, he then sells 50 more candle sets each week. A function can be used to model the relationship between the candlemaker's weekly revenue, R(x), after x one-dollar decreases in price.

R(x) = -50x2 + 300x + 2000

Maximum revenue of $2450 with x = 3

Step-by-step explanation:

For each 1$ reduced of the price, he sells 50 more candle sets, so if he reduces x times the price by 1$, the final price will be:

price = 10 - x

And the number of sets sold will be:

sets = 200 + 50x

If the revenue is the price times the number of sets sold, we have that:

R(x) = (10 - x) * (200 + 50x)

R(x) = 2000 + 500x - 200x - 50x2

R(x) = -50x2 + 300x + 2000

To find the value of x that gives the maximum revenue, we use the formula of the vertex of the quadratic equation:

x_v = -b / 2a

x_v = -300 / (-100) = 3

And the maximum revenue is:

R(x_v) = -50*3^2 + 300*3 + 2000 = $2450

tickets for the harlem globetrotters

show at michigan state university in

2010 cost $16, $23, or, for vip seats, $40.

total revenue = 16x + 23y + 40z

if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, sales of all three kinds of tickets would

total $46,575.

16x + 23y + 40z = 46575, how many of each kind of ticket would

have been sold?

solve for x, y and z

x − 9z = 0

x − y − z = 55

16x + 23y + 40z = 46575

x = 1170

y = 985

z = 130

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