Analysis Of Profit Function Based On Item Sales

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AnalysisofProfitFunctionBasedonItemSalesAnnualprofitinthousandsofdollarsisgivenbythefunction,P(x)=100*sqrt(x–5)+3000,wherexisthenumberofitemssold,x≥5.1.Describethemeaningofthenumber5intheformula.Answer:The number 5 in the formula P(x)=100x−5+3000P(x) = 100\sqrt{x-5} + 3000represents the minimum number of items that must be sold for the profit function to be valid.Explanation:•The formula involves the square root function,x−5\sqrt{x-5}, and for the square root tobe real and valid, x−5x-5 must be non-negative. This means x≥5x\geq 5 to ensure thatthe expression inside the square root is non-negative and the profit function can becomputed.•At x=5x = 5, the expression x−5\sqrt{x-5} becomes 5−5=0=0\sqrt{5-5} =\sqrt{0} = 0,meaning that when 5 items are sold, the profit is 30003000 thousand dollars (because theadditional profit term, 100x−5100\sqrt{x-5}, is 0).Conclusion:The number 5 in the formula sets the threshold for the number of items sold, indicating thatsales must be at least 5 for the profit function to apply and start generating a profit above thebase amount of 3000 thousand dollars. It essentially represents the starting point for calculatingthe profit.2.Describethemeaningofthenumber3000intheformula.Useacompletesentenceorsentences.Answer:The number 3000 in the formula P(x)=100x−5+3000P(x) = 100\sqrt{x-5} + 3000represents the base profit in thousands of dollars that the company earns regardless of thenumber of items sold. This is the fixed amount of profit the company earns when no additionalitems are sold, corresponding to the situation where x=5x = 5. It can be seen as the starting orguaranteed profit, even before any sales generate additional profit based on the number of itemssold.3.Findtheprofitfor6differentvaluesofx(showyourwork).PLEASEusex=5,69,105,230,366,and489andmakeatableusingMicrosoftExcel.Answer:To find the profit foreach value of xx, you can follow these calculations and create atable in Excel:

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