MAT135H1 Lecture 10: 3.4 Optimization in Economics and Science (3)

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Published on 22 Sep 2020
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3.4 Optimization in Economics and Science
In business, optimization involves maximizing profits and minimizing costs
! Revenue = (Price per unit) x (Number of units sold)
! Profit = Revenue Costs
Example 1: A commuter train carries 2000 passengers daily from the suburbs into the city. The cost to ride the train is
$7.00 per person. Market research shows that 40 fewer people would ride the train for each $0.10 increase in fare, and
40 more people would ride the train for each $0.10 decrease. If the capacity of the train is 2600 passengers, and
carrying less than 1600 passengers means costs would exceed revenue, what fare should the railway charge to get the
largest possible revenue?
Price of tickets sold
7.00 2000
0.10 YO
OIO t40
let number of price increments decrements
Rxprice xof ticketssold
RCx 7to Ix 2000 40ns
Pfx 14000 280 Xt200 4X
pix 14000 80 42RC10 14000 80
40 4G
Rxso 8x 14400 max
revenue
080 six RC15 14000 80C
15 4G
iEa in iii2soo
at xto price 710.1410
6.00
so The ticketprice forMax
Domain revenueis 6.00
2000 40XI2600 2000 40
21600
40xE2600 2000 Yox 400
III Ee To aTo
x15 XE10
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