The UofToys company has a factory that produces toy trucks and toy cars only. The total number of toys the factory has to produce over certain period of time is 250. An analysis reveals that the production time (in seconds) to produce x trucks is given by a function 1 Ttruck (x) 100 the production time (in seconds) to produce x cars is given by a function Tear (x) x² +90. = -x3 + 100. (a) How many toy trucks and toy cars should the factory produce to minimize the total production time? (b) The company is selling each toy truck for 1000 cents and each toy car for 1500 cents. The production cost of trucks and cars is 1 cent per second of production time: that is, for example, it costs Tear (x) cents to produce x cars. How many toy trucks and toy cars should the factory produce to maximize the profit? Explain your steps.
The UofToys company has a factory that produces toy trucks and toy cars only. The total number of toys the factory has to produce over certain period of time is 250. An analysis reveals that the production time (in seconds) to produce x trucks is given by a function 1 Ttruck (x) 100 the production time (in seconds) to produce x cars is given by a function Tear (x) x² +90. = -x3 + 100. (a) How many toy trucks and toy cars should the factory produce to minimize the total production time? (b) The company is selling each toy truck for 1000 cents and each toy car for 1500 cents. The production cost of trucks and cars is 1 cent per second of production time: that is, for example, it costs Tear (x) cents to produce x cars. How many toy trucks and toy cars should the factory produce to maximize the profit? Explain your steps.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 2. The UofToys company has a factory that produces toy trucks and toy cars only. The total
number of toys the factory has to produce over certain period of time is 250.
An analysis reveals that
the production time (in seconds) to produce x trucks is given by a function
1
= -x+100.
100
the production time (in seconds) to produce x cars is given by a function
Tear (x) = x² + 90.
Ttruck (x):
How many toy trucks and toy cars should the factory produce to minimize the total
production time?
(b) The company is selling each toy truck for 1000 cents and each toy car for 1500 cents.
The production cost of trucks and cars is 1 cent per second of production time: that is,
for example, it costs Tear (x) cents to produce x cars.
How many toy trucks and toy cars should the factory produce to maximize the profit?
Explain your steps.
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