Answer:
The annual profit if the baker sells 400 pies would be US$ 12,800
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Annual profit in dollars from selling pies using p n( ) = 52n − 0.05n² , where n is the number of pies sold
Annual sales of the baker = 400 pies
2. Let's solve p for 400 pies
p n( ) = 52n − 0.05n²
p (n₄₀₀) = 52 * 400 − 0.05 * 400²
p (n₄₀₀) = 20,800 − 0.05 * 160,000
p (n₄₀₀) = 20,800 − 8,000
p (n₄₀₀) = 12,800
The annual profit if the baker sells 400 pies would be US$ 12,800
The annual profit that the baker will make selling 400 pies will be $12,800
[tex]p(n) = 52n - 0.05n^2[/tex]
When he sells 400 pies, that means the value of n will be 400 here and the profit will be p(400).
[tex]p(n) = 52n + 0.05n^2\\p(400) = 52 \times 400 - 0.05 \times {400}^2\\p(400) = 20800 - 0.05 \times 160000\\p(400) = 20800 - 8000\\p(400) = 12800[/tex]
That means, total annual profit that baker will make will be $12,800.
Thus, the annual profit that the baker will make selling 400 pies will be $12,800
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