Touchie publishes comic books. The only inputs he needs are old jokes and cartoonists. His production function is Q $=0\mathrm{.}1$J $1/2$L $3/4,$ where J is the number of old jokes used, L the number of hours of cartoonists$$ labor used as inputs, and Q is the number of comic books produced. Assume that old jokes can be purchased for $$1$ each and that the wage rate of cartoonists$$ labor is $$2.($a$)$ Suppose that in the short run, Touchie is stuck with exactly $100$ old jokes $($for which he paid $$1$ each$)$ but is able to hire as much labor as he wishes. Write down Touchie$$s short$-$run total cost as a function of his output. $($b$)$ What is his short$-$run marginal cost function? $($c$)$ What is his short$-$run average cost function?