Please provide an explanation, thank you

I. True or false with justification, use graphical argument as appropriate. (It is not sufficient to state whether the statement is true or false, or even to correct it if it is false, in all cases you must justify your answer.) 1. A firm with a production function given by Y = min[3x1, x2], where x and y are two factors of production, faces factor prices of x = 2 and of y = 3. Its average cost of production is equal to 11/3. 2. The conditional factor demand function for factor 1 is a function x1(WI, w2, y) that tells the ratio of price to output for an optimal factor choice of the firm. 3. If there are increasing returns to scale, then average costs are a decreasing function of output. 4. The production function f(x, y) = x2+ y has increasing returns to scale. 5. If the value of the marginal product of labor exceeds the wage rate, then a competitive, profit-maximizing firm would want to hire less labor