Mack is starting a new business called River Adventures which will provide canoes and kayaks to people for daily rental. He has $45,000 available for purchasing the boats, and he has storage for up to 65 total boats. A canoe costs $600 and will rent for $25 a day, while a kayak costs $750 and will rent for $30 a day. Determine the number of canoes and kayaks he should buy in order to earn the highest daily revenue, assuming all boats are rented out each day.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Mack is starting a new business called River Adventures which will provide canoes and kayaks to people for daily rental. He has $45,000 available for purchasing the boats, and he has storage for up to 65 total boats. A canoe costs $600 and will rent for $25 a day, while a kayak costs $750 and will rent for $30 a day. Determine the number of canoes and kayaks he should buy in order to earn the highest daily revenue, assuming all boats are rented out each day.
Set-up this linear programming problem.
Let x be the number of canoes he buys, let y be the number of kayaks he buys, and let R be his daily revenue (in $).
The correct set-up is
- A.
Maximize R = 25x + 30y
Subject to 600x + 750y ≥ 45,000
x + y ≥ 65
x ≥ 0, y ≥ 0
- B.
Maximize R = 600x + 750y
Subject to 25x + 30y ≥ 45,000
x + y ≥ 65
x ≥ 0, y ≥ 0
- C.
Maximize R = x + y
Subject to 600x + 750y ≤ 45,000
25x + 30y ≤ 65
x ≥ 0, y ≥ 0
- D.
Maximize R = 25x + 30y
Subject to 600x + 750y ≤ 45,000
x + y ≤ 65
x ≥ 0, y ≥ 0
- E.
Maximize R = 600x + 750y
Subject to 25x + 30y ≤ 45,000
x + y ≤ 65
x ≥ 0, y ≥ 0
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