[From: ] [author: ] [Date: 12-06-02] [Hit: ]
the company has to increase the ticket price by \$5. Explain how to determine the number of empty seats that the bus should run in order to maximize profit.Can someone help me with this question??? Please and thankyou!......
it costs a bus company \$225 to run a minibus on a ski trip plus \$30 per. passenger. The bus has seating capacity for 22 people. The company charges \$60 per fare if the bus is full. For each empty seat, the company has to increase the ticket price by \$5. Explain how to determine the number of empty seats that the bus should run in order to maximize profit.

Can someone help me with this question??? Please and thankyou!~

-
Cost= C= 225+30x , Where x = number of passengers:
x = 22-n Where n= number of empty seats

C= 225+30(22-n)

C= 885-30n

Now for revenue, a full bus is 60 dollars for each of 22 passengers= 60(22)
But with n empty seats, number of passengers is 22-n, and price is 60+ 5n

Revenue = R= (60+5n)(22-n)

R= 1320+ 50n -5n^2

Profit= P= R- C = (1320+50n -5n^2 ) - (885-30n)

P= -5n^2 + 80n + 435

Notice this is a parabola that opens down, so the maximum occurs at the vertex.

n= -b/(2a)= -80/(2*-5)= 8

There should be 8 empty seats to maximize profit.

Hoping this helps!
1
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "http://www.science-mathematics.com/Mathematics/201206/32395.htm", "fetch_time": 1516773495000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2018-05/segments/1516084893397.98/warc/CC-MAIN-20180124050449-20180124070449-00521.warc.gz", "warc_record_offset": 560059242, "warc_record_length": 4740, "token_count": 388, "char_count": 1270, "score": 4.1875, "int_score": 4, "crawl": "CC-MAIN-2018-05", "snapshot_type": "latest", "language": "en", "language_score": 0.9027395844459534, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00034-of-00064.parquet"}