A firm produces yoghurt (y), for which it uses two inputs, milk (m) and labor (I). The production function of the firm is given by y(m, l) = m^1/2 * l^0.25. Assume for now that in the short run, the amount of labor the firm uses is fixed at l= 256, so the single variable input of the firm is milk. Now use this info to write down the short-run, single-variable production function y(m).

What is the slope of this short-run, single-variable production function at the point m=5?

Now assume that instead of the above, the market price of youghurt is p=8 and the market price of milk is r=2. What is the (short-run) profit maximizing youghurt output of the firm?