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).

Assume that the market price of yoghurt (for which the firm is able to sell its output) is equal to p=7, and the market price of milk (that the firm has to pay for as input) is equal to r=4.

Write down the equation of the isoprofit lines. (Hint: write down the profit function and then transform it to the form y(ir, m). What is the slope of these isoprofit lines if you plot them in the m-y space?