Suppose The Rate Of Training Hours Is Given By: HI


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Suppose the rate of training hours is given by: HI(x)=10-x, where x is the number of units a worker can make in an hour. How many hours of training are necessary for the worker to produce the first 5 units?


Answer No.1


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Given that, the rate of training hours function is H'(x)=10-x dH/dx=10-x this is fister order differtial equation, which can be solve by variable seperable method integral of(dH)=integral of(10-x) H(x)=10x-(x^2/2)+c ......(1) where c is an integration constant, to find c, we shall apply the initial conditions, that are, at time x=0, H(x)=0 that means, no units made by the worker initially, put x=0 and H=0 in (1), we get, c=0, now (1) becomes, H(x)=10x-(x^2/2).....(2) put x=5 in (2), to evaluate the no hours taken by the worker to make 5 units, therefore, H(5)=10*5-(5^2/2) H(5)=37.5 hours, that is, the worker takes 37.5 hours to make 5 units.

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