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?
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 maximumprofit?
C = 350,000 – 190x +0.035x2 How many units should be produced each day to yield a minimumcost?
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 maximumprofit?
P = 290 + 90x –0.5x2

Explanation / Answer

Since both these functions are quadratic they have a vertexwhich for the general quadractic ax^2 + bx + c the x locationof the vertex is located by the formula x = -(b/(2a)) Sincethe cost parabola opens up the vertex will yield the minimum, andsince the profit parabola opens down its vertex will give themax. So for Cost x = 190/(2*.035)=190/.07˜2,714 a similar calculation will yield the x that produces maxprofit

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