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#### HighAllegiant

##### New member

- Jun 26, 2012

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**[SOLVED] Managerial Economics Problem**

SOLVED

I already solved (a) by finding the derivative with respect to (x,y) and equating to 0.A firm has decided through regression analysis that its sales (S) are a function ofthe amount of advertising (measured in units) in two different media, television (x) and magazines (y):

(a) Find the level of TV and magazine advertising units that maximizes the firm's sales.

S(x, y) = 100 – x^{2}+ 30x – y^{2}+ 40y

(c) Give an economic interpretation for the value of the Lagrangian Multiplier obtained in part (b) above.

(b) Suppose that the advertising budget is restricted to 31 units. Determine the level of advertising (in units) that maximizes sales subject to this budget constraint.

(a) X

^{*}= 15, Y

^{*}= 20

My prof provided the answer to (b) and I have absolutely no idea to how he arrived at it.

I assumed the the Income(M)=31 but without any given prices for (x,y), I cannot seem to apply it into a Lagrangian method.

(I'm assuming I use the Lagrangian method because it was the most recent lecture to this question. (c) also asks a follow up question which requires the Langrangian multiplier.)

Could anyone help me?

(b) X

^{*}= 13, Y

^{*}= 18

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