Question

# A manufacturer produces two products, Product A and Product B. The weekly profit function, in dollars,

is

*P*(*x*,*y*)= 560*x*+20*xy*−20*x*^{2}−6*y*^{2}

where *x *and *y *are units of each product in thousands. Determine how many units of each product should be produced and sold weekly in order to maximize the manufacturer's total weekly profit and the maximum value of the total weekly profit. Follow the steps:

(a) The only critical point of *P*

is (*x*_{c}, *y*_{c}) = (__ ,__ ).

(c) Therefore in order to maximize the manufacturer's total weekly profit,__units of Product A and__units of Product B should be produced and sold per week.

(d) Now, plug *x *=__ and *y* =__ into the function *P*(*x*, *y*) we obtain that the maximum weekly profit is $__ .

#### Top Answer

(a) The only critical point of P is ( x c ; y c ) = ( 8 4 ; 1 4 0 ) (c)... View the full answer