Time In an exercise earlier in this chapter, we saw that the time (in hours) that a branch of Amalgamated Entities needs to spend to meet the quota set by the main office can be approximated by
$$T(x, y)=x^{4}+16 y^{4}-32 x y+40$$
where $x$ represents how many thousands of dollars the factory spends on quality control and $y$ represents how many thousands of dollars they spend on consulting. Find the average time if the amount spent on quality control varies from $\$ 0$ to $\$ 4000$ and the amount spent on consulting varies from $\$ 0$ to $\$ 2000$ . (Hint: Refer to Exercises $61-64 . )$