A manufacturer of two products $($Widgets and Gadgets$)$ makes a profit of $$170$ for each widget sold and $$120$ for

each gadget sold. However, production of these products generates hazardous waste charges at the rate of $1w^2$

$($where $W$ is the number of Widgets produced$)$ and $1G^3($where $G$ is the number of Gadgets produced$).$ The

manufacturer has ample supplies of all raw materials and can sell all the Widgets and Gadgets it produces. The firm

has sufficient capacity to produce any realistic quantity of both products.

What is the optimal quantity of each product to produce? $($Round your answers to $1$ decimal place.$)$

Widgets and

Gadgets

What is the maximum profit the manufacturer can earn? $($Round your answer to $2$ decimal places.$)$

Maximum profit