The UofToys company has a factory that produces toy trucks and toy cars only. The total umber 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 a trucks is given by a function 1 Ttruck (2) = -2³ +100. 100 the production time (in seconds) to produce x cars is given by a function Tear (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 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 (2) 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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