A university is considering hiring ONE new employee, either a professor or a jan

Question

A university is considering hiring ONE new employee, either a professor or a janitor, to help complete a large scale project. The cost (in dollars) of the project is given by C(x, y) = -38 x^2 + 14 x/y +1254 ln(x y) - 351 x - 35 y + 3000 where x represents the number of professors and y represents the number of janitors working on the project. Use marginal cost to determine which of the following options is the MOST cost effective if 19 professors and 10 janitors are currently employed. It is NOT cost effective for the university to hire at There is not enough information provided.

Explanation / Answer

Ans-a)It is not cost effective for the university to hire.

Explanation-C(x,y)=-38x2+14x/y+1254in(x,y)-351x-35y+3000

dC/dx=-76x+14/y+1254/x-351=0...............(1)

dC/dy=(-1)14xy-2+1254/y-35=0..................(2)

-14x/y2+1254/y-35=0

Putting value of x=professor=19,y=Janitor=10 in both equations we have,.

Or,-1444+1.4+66-351is not equal to 0.

-2.66+125.4-35 is not equal to o.

In both equations marginal cost condition is not fulfilled.

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