Question

) POLYNOMIAL AND RATIONAL FUNCTIONSVord problem involving the maximum or minimum of a quadrati.

Answer 1

Case: Minimum and Maximum functions

Given:

`\begin{gathered} C(x)=0.8x^2-352x+58,583 \\ \end{gathered}`

Required: To find the minimum Unit cost

Method: we apply completing square on the function

Step 1: First we find the square of half the coefficient of x

`\begin{gathered} C(x)=\text{ 0.8x}^2-352x+58583 \\ C(x)=\text{ 0.8\lparen x}^2-440x+73228.75) \\ (1)/(2)(440)=\text{ 220}^2\Rightarrow\text{ 48400} \end{gathered}`

Step 2: Add and subtract the value to the Right Hand Side

`\begin{gathered} C(x)=\text{ 0.8\lparen x}^2-440x+48400-48400+73228.75) \\ Completing\text{ squares in the bracket} \\ C(x)=\text{ 0.8\lbrack\lparen x-220\rparen}^2+24828.75] \\ C(x)=0.8(x-220)^2+\text{ 19863} \end{gathered}`

Step 3: From the equation

The quantity need to be produced to get the minimum unit cost is 220.

The value of the minimum cost therefore is obtained at C(220).

This would give:

C(220)= $19863

Final answer:

The minimum unit cost is $19863. Ignore the dollar sign($) when entering your answer.