1. A firm has the production function, f(x, y) = 20x^3/5y^2/5. The slope of the firm's isoquant at the point (x; y) = (80; 10) is: (Pick the closest one.) answer is -0.19, please show steps and explain, thank you.

2. A firm has the production function f(X, Y ) = X^3/4Y^1/4 where X is the amount of factor x used and Y is the amount of factor y used. On a diagram we put X on the horizontal axis and Y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of -3. The straight line we drew: (ans is C, please show steps and explain.)

(a) is vertical.

(b) is horizontal.

(c) is a ray through the origin with slope 1.

(d) is a ray through the origin with slope 2.

(e) has a negative slope.

3. A firm has the production function f(x_1,x₂)=x₁^0.40x₂^0.20 . The isoquant on which output is 40^2/10 has the equation? the ans is x₂ = 40x₁^-0.20 please show steps and explain. 

4. A firm has a production function f(x, y) = 1(x^0.80+y^0.80)⁴ whenever x > 0 and y >0. When the amounts of both inputs are positive, this firm has: increasing returns to scale. Please explain.