A textile manufacturer has daily production costs as shown in theequation below,

Question

A textile manufacturer has daily production costs as shown in theequation below, where C is the total cost (in dollars) andx is the number of units produced. C = 350,000 – 190x +0.035x2 How many units should be produced each day to yield a minimumcost?



b. The profit P (in hundreds of dollars) that a companymakes depends on the amount x (in hundreds of dollars) thecompany spends on advertising according to the model shown below. P = 290 + 90x –0.5x2 What expenditure for advertising will yield a maximum profit?
1 dollars C = 350,000 – 190x +0.035x2 P = 290 + 90x –0.5x2

Explanation / Answer

C = 350,000 – 190x +0.035x2 This is an   x2   equation, soit is a parabola. To find the minimum of a parabola, you wantto find its vertex. The   x value of the vertex will give the # of unitsproduced, and the y value (or C value in thiscase) will give the total cost.      You can take the last 2 terms and"complete the square" if you like, but it's easier tojust graph it on a calculator and find the minimum thatway. On a TI calculator, type[2nd],[calc],[minimum].    If you have a TIcalculator and need help with it, send mea message. . Part b) P = 290 + 90x – 0.5x2 Again, a parabola.   Graph it and find the xvalue at which the maximum occurs.

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