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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?