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4. You are manufacturing ceramic lawn ornaments. After several months, your accountant tells you that your profit, P (n), can be modeled by P(n) = -0.002n + 6.5n+1100, where nis the number of ornaments sold each month. a) Based on this model if your company manufactures 1000 lawn ornaments, how much profit would you expect to earn? [2] b) If you want to earn at least $6000 in profit, what is the minimum number of ornaments your company must manufacture and sell to reach this goal? (round to a whole number) [4]

Answer :

The profit fuction is given as,

[tex]P(n)=-0.002n+6.5n+1100[/tex]

(a):

If the value of n=1000 the profit can be determined as,

[tex]\begin{gathered} P(1000)=-0.002\times1000+6.5\times1000+1100 \\ =7598 \end{gathered}[/tex]

Thus, the required profit is 7598.

(b):

If the value of profit is $6000 then the minimum number of ornamets can be determined as,

[tex]\begin{gathered} 6000=-0.002n+6.5n+1100 \\ 4900=6.498n \\ n=754.078\approx755 \end{gathered}[/tex]

Thus, the required number of minimum ornamets is 755.

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