12:54
Finite Mathematics and Calculus with Applications
Production A manufacturing firm estimates that its total production of automobile batteries in thousands of units is $$
f(x, y)=3 x^{1 / 3} y^{2 / 3}
$$
where $x$ is the number of units of labor and $y$ is the number of units of capital utilized. Labor costs are $\$ 80$ per unit, and capital costs are $\$ 150$ per unit. How many units each of labor and capital will maximize production, if the firm can spend $\$ 40,000$ for these costs?