Verify the following using Excel Solver. Please provide detailed screen shots from Solver.
Using the Lagrangean multiplier approach calculate the optimal (i.e., service
maximizing) combination of medical and social worker staff. Determine the
optimal amount of service provided by BF.
Output function: Z = M + 0.5S + 0.5MS - S^2 , Cost function: 30000S + 60000M = 1200000
For langrangean function, we need to equate the derivative of output function wrt to M and S respectively with the MC wrt to M and S, we get
30000S = 30000n and 30000M = 60000n
S = n and M = 2n
30000n + 60000(2n) = 1200000
30000n + 120000n = 1200000
150000n = 1200000
n = 120/15 = 8
Thus S = 8 and M = 2(8) = 16
Put these values of S and M in Z, we get
Z = 16 + 0.5 (8) + 0.5 (16*8) - 8^2 = 16 + 4 + 64 - 64 = 20
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