SOLUTION: Sophia owns a cheese factory. The amount of cheese, in kilograms, that she sells in one week, Q, is given by Q = 882 - 45p, where p is the price of a kilogram of cheese in euros

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Question 1125278: Sophia owns a cheese factory. The amount of cheese, in kilograms, that she sells in one week, Q, is given by
Q = 882 - 45p, where p is the price of a kilogram of cheese in euros (EUR).
Sophia earns (p - 6.80) euros of profit for each kilogram of cheese sold.
-What price should Sophia set for her cheese so that she earns a maximum profit?
-What is her maximum profit?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Her total profit, +P+, is:
+Q%2A%28+p+-+6.8+%29+=+%28+882+-+45p+%29%2A%28+p+-+6.8+%29+
+P+=+882p+-+45p%5E2+-+5997.6+%2B+306p+
+P+=+-45p%5E2+%2B+1188p+-+5997.6+
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The maximum p-value is
+p%5Bmax%5D+=+-b%2F%28+2a%29+
+a+=+-45+
+b+=+1188+
+p%5Bmax%5D+=+-1188%2F%282%2A%28-45%29%29+
+p%5Bmax%5D+=+13.2+
Maximum profit is at the price of 13.2 euros
———————
+P%5Bmax%5D+=+-45%2A13.2%5E2+%2B+1188%2A13.2+-+5997.6+
+P%5Bmax%5D+=+-7840.8+%2B+15681.6+-+5997.6+
+P%5Bmax%5D+=+17524.8+
17,524.8 euros is the maximum profit
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Check the math & get 2nd opinion if needed