Suppose a firm has a production function q $=5$ L $0\mathrm{.}6$K$0\mathrm{.}4,$ where L represents labor and K represents capital. The firm hires labor at a wage rate of w $=$ $$10$ and rents capital at a rate of r $=$ $$20.($a$)$ Determine the marginal product of labor $($MPL$)$ and the marginal product of capital $($MPK$)$ for this production function: MP L $=3\mathrm{.}0$ L $0\mathrm{.}4$ K$0\mathrm{.}4,$ MPK $=2\mathrm{.}0$ L $0\mathrm{.}6$ K$0\mathrm{.}6(2$ points$)($b$)$ Determine the slope of the isocost curves for this firm: $$ w r $=0\mathrm{.}5(1$ point$)($c$)$ If the goal is to produce $100$ units, what is the optimal input combination of labor and capital?