At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly

Question

At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of acetate fibers that can be produced is given by the function:

z=f(x,y)=10000x+4000y+5x2y?6x3z=f(x,y)=10000x+4000y+5x2y-6x3

Where:
zz = the weekly # of pounds of acetate fiber
xx = the # of skilled workers at the plant
yy = the # of unskilled workers at the plant


Determine the following:

A) The weekly number of pounds of fiber that can be produced with 13 skilled workers and 35 unskilled workers.

Answer =  pounds

B) Find an expression (fxfx) for the rate of change of output with respect to the number of skilled workers.

Answer = fx=fx=     

C) Find an expression (fyfy) for the rate of change of output with respect to the number of unskilled workers.

Answer = fy=fy=     

D) Find the rate of change of output with respect to skilled workers when 13 skilled workers and 35 unskilled workers are employed. (Your answer will be a number.)

Answer =  weekly pounds per skilled worker

E) Find the rate of change of output with respect to unskilled workers when 13 skilled workers and 35 unskilled workers are employed. (Your answer will be a number.)

Answer =  weekly pounds per unskilled worker

At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of acetate fibers that can be produced is given by the function: z=f(z, y) = 10000z + 4000y + 5Py-e2 Where: the weekly # of pounds of acetate fiber z = the # of skilled workers at the plant y = the # of unskilled workers at the plant Determine the following: A) The weekly number of pounds of fiber that can be produced with 13 skilled workers and 35 unskilled workers. Answer B) Find an expression ( for the rate of change of output with respect to the number of skilled workers Answer = f,-! C) Find an expression (f,) for the rate of change of output with respect to the number of unskilled workers. pounds Answer - Preview Answer- Answer - f- Preview D) Find the rate of change of output with respect to skilled workers when 13 skilled workers and 35 unskilled workers are employed. (Your answer will be a number.) Answer ]weekly pounds per skilled worker E) Find the rate of change of output with respect to unskilled workers when 13 skilled workers and 35 unskilled workers are employed. (Your answer will be a number) Answer weekly pounds per unskilled worker

Explanation / Answer

A) put x = 13 and y = 35 in f ( x , y) = 10000x 13 + 4000 x 35 + 5 x 169 x 35 - 6 x 13 x 13 x13 = 286393 pounds

b ) and D) differentiate f ( x , y ) with respect to x : fx = 10000 + 10 xy - 18 x2

put x = 13 and y = 35 : 10000 + 10 x 13 x 35 - 18 x169 = =11508 pounds

C ) and E 0 differentiate partially w r t to y : fy : 4000 + 5 x2

put x = 13 and y = 35 : : 4000 + 5 x 169 4845 pounds

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