Question

A small company builds tables and chairs. Let x equal the number of tables made each hour and y equal the number of chairs made each hour. If hourly revenue is given by LaTeX: z=R\left(x,y\right)=-2x^2+40x-2y^2+8y+1000z = R ( x , y ) = − 2 x 2 + 40 x − 2 y 2 + 8 y + 1000, find the maximum revenue attainable and find the number of tables and chairs that should be produced to yield that maximum revenue.

Give the two first partials:

Rx(x,y)=

Ry(x,y)=

List all critical points and the value of the D test for each critical point. If there is more than one critical point, separate them with commas and a space. Use the format (x1,y1) D-test_value1, (x2,y2) D-test_value2, etc.

Give the optimal value in coordinate form (x,y,z).

Answer 1

maximum revenue attainable = 1208

number of tables to produce = 10

number of chairs to produce = 2