Toy's company has a factory that produces toy trucks and toy cars. The total number of toys the factory has to produce over a certain period of time is 300. An analysis reveals that • the production time (in seconds) to produce x number of trucks is given by a function Ttruck(x) = (1/100)x3 + 100. • the production time (in seconds) to produce x number of cars is given by a function Tcar(x) = x2 + 90. (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 2500 cents and each toy car for 2000 cents. The production cost of trucks and cars is 1 cent per second of production time (= costs Tcar(x) cents to produce x cars). How many toy trucks and toy cars should the factory produce to maximize the profit?
Toy's company has a factory that produces toy trucks and toy cars. The total
number of toys the factory has to produce over a certain period of time is 300.
An analysis reveals that
• the production time (in seconds) to produce x number of trucks is given by a function
Ttruck(x) = (1/100)x3 + 100.
• the production time (in seconds) to produce x number of cars is given by a function
Tcar(x) = x2 + 90.
(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 2500 cents and each toy car for 2000 cents.
The production cost of trucks and cars is 1 cent per second of production time (= costs Tcar(x) cents to produce x cars).
How many toy trucks and toy cars should the factory produce to maximize the profit?
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