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VI VI We will use linear programming to answer this question in Example 1. EXAMPLE 1 Canoe Rentals Thomas Pinedo plans to start a new business called River Explorers, which will rent cano and kayaks to people to travel 10 miles down the Clarion River in Cook Forest State Par He has $45,000 to purchase new boats. He can buy the canoes for $600 each and the kayal for $750 each. His facility can hold up to 65 boats. The canoes will rent for $25 a day, ar the kayaks will rent for $30 a day. How many canoes and how many kayaks should he bu tuto earn the most revenue if all boats can be rented each day? IT SOLUTION Let x represent the number of canoes and let y represent the number of kayak Summarize the given information in a table. Dividing +24=300 cRental Information bon (2 odTslo sulev mu em imo Canoes The oumb Kayaks Total Number of Boats 65 Cost of Each $750 $45,000 Revenue $25 $30 ench pig $40 1f The constraints, imposed by the number of boats and the cost, correspond to the rows in th table as follows. y< 65 buogr tot cacp parcy o 600x + 750y < 45,000 uam woH ixem a0Y Dividing both sides of the second constraint by 150 gives the equivalent inequality 4x + 5y < 300. Since the number of boats cannot be negative, x 2 0 and y 2 0. The objective function to be maximized gives the amount of revenue. If the variable z represents the total revenue, the objective function is LGPILICIOO aldonggimz= 25x + 30y. %3D og In summary, the mathematical model for the given linear programming problem is as deid follows:g s Maximize z = 25x + 30y %3D subject to: eleminA ms3 x + y < 65 Number of boats 4x + 5y < 300 Cost (reduced) (3)

VI VI We will use linear programming to answer this question in Example 1. EXAMPLE 1 Canoe Rentals Thomas Pinedo plans to start a new business called River Explorers, which will rent cano and kayaks to people to travel 10 miles down the Clarion River in Cook Forest State Par He has $45,000 to purchase new boats. He can buy the canoes for $600 each and the kayal for $750 each. His facility can hold up to 65 boats. The canoes will rent for $25 a day, ar the kayaks will rent for $30 a day. How many canoes and how many kayaks should he bu tuto earn the most revenue if all boats can be rented each day? IT SOLUTION Let x represent the number of canoes and let y represent the number of kayak Summarize the given information in a table. Dividing +24=300 cRental Information bon (2 odTslo sulev mu em imo Canoes The oumb Kayaks Total Number of Boats 65 Cost of Each $750 $45,000 Revenue $25 $30 ench pig $40 1f The constraints, imposed by the number of boats and the cost, correspond to the rows in th table as follows. y< 65 buogr tot cacp parcy o 600x + 750y < 45,000 uam woH ixem a0Y Dividing both sides of the second constraint by 150 gives the equivalent inequality 4x + 5y < 300. Since the number of boats cannot be negative, x 2 0 and y 2 0. The objective function to be maximized gives the amount of revenue. If the variable z represents the total revenue, the objective function is LGPILICIOO aldonggimz= 25x + 30y. %3D og In summary, the mathematical model for the given linear programming problem is as deid follows:g s Maximize z = 25x + 30y %3D subject to: eleminA ms3 x + y < 65 Number of boats 4x + 5y < 300 Cost (reduced) (3)

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 21E: Making furniture Two woodworkers, Chase and Devin, get 100 for making a table and 80 for making a...
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VI VI We will use linear programming to answer this question in Example 1. EXAMPLE 1 Canoe Rentals Thomas Pinedo plans to start a new business called River Explorers, which will rent cano and kayaks to people to travel 10 miles down the Clarion River in Cook Forest State Par He has $45,000 to purchase new boats. He can buy the canoes for $600 each and the kayal for $750 each. His facility can hold up to 65 boats. The canoes will rent for $25 a day, ar the kayaks will rent for $30 a day. How many canoes and how many kayaks should he bu tuto earn the most revenue if all boats can be rented each day? IT SOLUTION Let x represent the number of canoes and let y represent the number of kayak Summarize the given information in a table. Dividing +24=300 cRental Information bon (2 odTslo sulev mu em imo Canoes The oumb Kayaks Total Number of Boats 65 Cost of Each $750 $45,000 Revenue $25 $30 ench pig $40 1f The constraints, imposed by the number of boats and the cost, correspond to the rows in th table as follows. y< 65 buogr tot cacp parcy o 600x + 750y < 45,000 uam woH ixem a0Y Dividing both sides of the second constraint by 150 gives the equivalent inequality 4x + 5y < 300. Since the number of boats cannot be negative, x 2 0 and y 2 0. The objective function to be maximized gives the amount of revenue. If the variable z represents the total revenue, the objective function is LGPILICIOO aldonggimz= 25x + 30y. %3D og In summary, the mathematical model for the given linear programming problem is as deid follows:g s Maximize z = 25x + 30y %3D subject to: eleminA ms3 x + y < 65 Number of boats 4x + 5y < 300 Cost (reduced) (3)
Transcribed Image Text:VI VI We will use linear programming to answer this question in Example 1. EXAMPLE 1 Canoe Rentals Thomas Pinedo plans to start a new business called River Explorers, which will rent cano and kayaks to people to travel 10 miles down the Clarion River in Cook Forest State Par He has $45,000 to purchase new boats. He can buy the canoes for $600 each and the kayal for $750 each. His facility can hold up to 65 boats. The canoes will rent for $25 a day, ar the kayaks will rent for $30 a day. How many canoes and how many kayaks should he bu tuto earn the most revenue if all boats can be rented each day? IT SOLUTION Let x represent the number of canoes and let y represent the number of kayak Summarize the given information in a table. Dividing +24=300 cRental Information bon (2 odTslo sulev mu em imo Canoes The oumb Kayaks Total Number of Boats 65 Cost of Each $750 $45,000 Revenue $25 $30 ench pig $40 1f The constraints, imposed by the number of boats and the cost, correspond to the rows in th table as follows. y< 65 buogr tot cacp parcy o 600x + 750y < 45,000 uam woH ixem a0Y Dividing both sides of the second constraint by 150 gives the equivalent inequality 4x + 5y < 300. Since the number of boats cannot be negative, x 2 0 and y 2 0. The objective function to be maximized gives the amount of revenue. If the variable z represents the total revenue, the objective function is LGPILICIOO aldonggimz= 25x + 30y. %3D og In summary, the mathematical model for the given linear programming problem is as deid follows:g s Maximize z = 25x + 30y %3D subject to: eleminA ms3 x + y < 65 Number of boats 4x + 5y < 300 Cost (reduced) (3)
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