Mathematics 1 Deneme Sınavı Sorusu #1357157

The demand equation for the firm Comp-M is p(x)=150-2x and the cost function is C(x)=120+60x-x² for 0?x?40. If the government imposes a tax of 4 TL per unit quantity produced on Comp-M, what is the price that maximizes the profit?

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Yanıt Açıklaması:

Since P(x)=R(x)-C(x), according to the given information we can write P(x)=(150-2x)x-(120+60x-x² )=-x²+90x-120. Now, since there is an extra of 4 TL tax the modified profit function is P(x)=-x²+(90-4)x-120=-x²+86x-120. The price that maximizes the profit is where the derivative is zero, i.e., P' (x)=-2x+86=0 which is x=43 TL. We insert this value in the price so that p(43)=150-2·43=64 TL.

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SORUNUN CEVABI: C

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Mathematics 1 Deneme Sınavı Sorusu #1357157

The demand equation for the firm Comp-M is p(x)=150-2x and the cost function is C(x)=120+60x-x2 for 0?x?40. If the government imposes a tax of 4 TL per unit quantity produced on Comp-M, what is the price that maximizes the profit?

SORUNUN CEVABI: C

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The demand equation for the firm Comp-M is p(x)=150-2x and the cost function is C(x)=120+60x-x² for 0?x?40. If the government imposes a tax of 4 TL per unit quantity produced on Comp-M, what is the price that maximizes the profit?