An engineering consulting firm has the following total & marginal product functions:

Q = 20E - E2 + 12T - 0.5T2 (total product function)

MPE = 20 - 2E and MPT = 12 - T (marginal productivity of E or T)

where: E = the number of engineers used and T = the number of technicians used on projects,

The wage paid to engineers is $4000, while technicians, who are not as skilled as engineers, receive $2000. The firm's budget on a particular project is $28,000. How many engineers and how many technicians should be hired in order to maximize production relative to their budget? Hint: Set up an equation that allocates engineers and technicians optimally first and solve in terms of one variable (E or T). Once you get that, then take the budget into account (by setting up a cost equation) so you can get the correct number of workers to use by doing substitution.