Each week, a manufacturer of chocolate cakes is able to produce f(HM) cakes if their employees work a total of H hours and they use their cake production machines for a total of M hours. The employees' wage is $19 per hour and due to electricity and maintenance, the machines cost about $30 per hour to run. Their operating budget is $10,000 per week. In order to determine how to maximize their production, they use the method of Lagrange multipliers. The solutions to the Lagrange multiplier equations are H = 400, M = 80, and = 5.

(a) If their weekly budget decreases by about $100, how will their weekly production be affected?
(b) Find the value of fu(400,80).
(c)In order verify that their solution does indeed lead to maximum production, they use the second derivative test. At the point (H, M) = (400, 80), they find that D = funfmm-(fam)? > 0 and fun >0. Should they be concerned?