Download WS 5.9 Optimization File

AP Calculus
WS 5.8 Optimization: Economic Applications Worksheet
Name: _______________________
1) The beverage industry in Canada produces over $10 billion worth of product annually. Based
on a 10-year study of production costs, a winery in the Niagara region has determined that the
cost of producing x bottles of wine is
C ( x)  12000  4 x  0.0002 x 2
Market research shows that the demand for the win is given by the price function
p( x)  12  0.0001x
Determine the production level that maximizes the revenue.
Determine the production level that maximizes the profit.
2) A textile manufacturer uses regression to determine that the cost of producing x meters
of woven fabric is
C ( x)  100  8x  0.1x 2  0.001x3
It forecasts it can sell the fabric for
p( x)  16  0.03x
Determine the production level that will give maximum profit.
3) A professional basketball team plays in a stadium that holds 23,000 spectators. Through
research, the marketing department has determined that the demand for tickets can be
modeled by p( x)  42000  400 x , where x is the price of a ticket. Based on this pattern,
how should ticket prices be set to maximize revenue?
AP Calculus
WS 5.8 Optimization: Economic Applications Worksheet
Name: _______________________
1) The beverage industry in Canada produces over $10 billion worth of product annually. Based
on a 10-year study of production costs, a winery in the Niagara region has determined that the
cost of producing x bottles of wine is
C ( x)  12000  4 x  0.0002 x 2
Market research shows that the demand for the win is given by the price function
p( x)  12  0.0001x
Determine the production level that maximizes the revenue.
Determine the production level that maximizes the profit.
2) A textile manufacturer uses regression to determine that the cost of producing x meters
of woven fabric is
C ( x)  100  8x  0.1x 2  0.001x3
It forecasts it can sell the fabric for
p( x)  16  0.03x
Determine the production level that will give maximum profit.
3) A professional basketball team plays in a stadium that holds 23,000 spectators. Through
research, the marketing department has determined that the demand for tickets can be
modeled by p( x)  42000  400 x , where x is the price of a ticket. Based on this pattern,
how should ticket prices be set to maximize revenue?