Imagine that a firm can use labor (L) or capital(K) to produce rocking chairs (Q) with the following production function Q=2L+5K.The wage (w) is $10 and the rate of capital (r) is $20. The target number of rocking chairs to produce is 30.

a) Find the optimal inputs in the long run. L*=____ and K*=____

b) Now for the SHORT RUN, imagine that K is fixed at a value of 2. What are the values of the short run optimal inputs? L*=____ and K*=____

c) If you were going to draw this question, your short-run solution in part (b) would lie on either theisocostor theisoquantcurve that you would drawn for the long-run solution in part (a).Which curve would it lie on? (write "isocost" or "isoquant")