A car is built using 4 wheels (W) and a body (B). Production function for cars (q) is given by = (, ) = min ( 1 4 , ). Price of a wheel is 5, and of a body is 100. Cars, wheels, and bodies are all infinitely divisible (meaning they can take any positive values, including integers and fractions).

a) When W=7, and B=2, what is the marginal product of a wheel? (1 pt.)

b) Draw an isoquant with q=10, and three separate isocost lines (one below, one through, and one above the isoquant). Make sure to label all intercepts and intersections. (5 pts.)

c) To create 10 cars, what is the minimized cost? (2 pts.)

d) Typical methods ( = or Lagrange) are not suitable to answer part c). Explain. In your answer, make sure to include the graph of appropriate isocost line(s), isoquant(s), and verbal interpretation of why typical methods would not work to find the cost minimizing inputs. (5 pts.)

e) What is the total cost function ()? (5 pts.)