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)
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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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