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Algebra
Pregunta

6. A small independent movie company determines th...

6. A small independent movie company determines the profit \( P \) for producing \( n \) DVD copies of a recent release is \( P = - 0.02 n ^ { 2 } + 3.40 n - 16 \) . 

\( P \) is the profit in thousands of dollars and \( n \) is in thousands of units. 

a. How many DVDs should the company produce to maximize the profit? 

b. What will the maximum profit be? 

Answer

a) to find the maximum, differentiate P w.r.t.n then set it to zero

dP/dn = -0.04n+3.40

 -0.04n+3.40=0

0.04n=3.40

n= 85 units

 

b) maximum profit 

P(85)= -0.02(85)^2 +3.40(85)-16 = $128.5

 

Solución
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