It takes Caroline 1 hr to ride the train to some place and 1.5 hr to ride the bus. Every week, she must make at least 8 trips to the place, and she plans to spend no more than 9 hr in travel time. If a train trip costs $6 and a bus trip costs $5, how many times per week should she ride each in order to minimize her cost?
She should ride the train for _ trips and the bus for _ trips in order to minimize her cost.

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03-07-2021
Mathematics

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It takes Caroline 1 hr to ride the train to some place and 1.5 hr to ride the bus. Every week, she must make at least 8 trips to the place, and she plans to spend no more than 9 hr in travel time. If a train trip costs $6 and a bus trip costs $5, how many times per week should she ride each in order to minimize her cost?
She should ride the train for _ trips and the bus for _ trips in order to minimize her cost.

Sagot :

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raphealnwobi raphealnwobi · Answer 1 · 2021-07-07T21:24:21-04:00

Answer:

She should ride the train for 6 trips and the bus for 2 trips in order to minimize her cost.

Step-by-step explanation:

Let x represent the number of times that she travels using the train and let y represent the number of times she travels using the bus. Since she makes at least 8 trips to the place, hence:

x + y ≥ 8

Also, she plans to spend no more than 9 hr in travel time. Hence:

x + 1.5y ≤ 9

x ≥ 0, y ≥ 0.

Plotting the above equations on geogebra online graphing tool, the solution is (6, 2), (8, 0) and (9, 0).

If a train trip costs $6 and a bus trip costs $5, The cost equation (C) is:

C = 6x + 5y

At point (6, 2): C = 6(6) + 5(2) = $46

At point (8, 0): C = 6(8) + 5(0) = $48

At point (9, 0): C = 6(9) + 5(0) = $54

Therefore the minimum cost is at (6, 2). She should ride the train for 6 trips and the bus for 2 trips in order to minimize her cost.

Sagot :

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