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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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