Sarah's Pretzel plant has the following short-run cost function:see below. whereqis Sarah's output level,wis the cost of a labor hour, andKis the number of pretzel machines Sarah leases.Sarah's short-run marginal cost curve issee below.At the moment, Sarah leases 10 pretzel machines, the cost of a labor hour is $6.85, and she can sell all the output she produces at $35 per unit.

a.If the cost per labor hour rises to $7.50, what happens to Sarah's optimal level of output and profitsthepriceofcapitalis $1andthepriceoflaboris$2.Findthecost-minimizingdemandsforKandL.

short run cost function: C(q,K) = (wq^3/1000K^1.5) + 50K

short run marginal cost function: MC(q,K) = 3wq^3/1000K^1.5