MAT 140 Spring Proctice Exam-Microsoft Word Home Insert Page Layout Refer s Cut

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MAT 140 Spring Proctice Exam-Microsoft Word Home Insert Page Layout Refer s Cut ences MailingsReviewVieww Find aBbCcDc AaBbccD AaBbC AaBbCc AaBbCcc AaB AaBbCcL AaBbCcD 1Nor mal 1NoSpo Heading 1 Heading 2 Heading 3 Copy ac Replace Paste Blu-b6X, Xa Aa,y.. . b. E Subtitle Subtie Em",-C Subtite Subtie Em... Change styles? Title Select- Font Paragraph Styles ral Editing 12. A mining company has determined that the cost C.in dollars per ton of mining a mineral is given by the function Cx) 0.2x2 6x 8, where x is the number of tons of the mineral mined. Find the number of tons of the mineral that should be mined to minimize the cost What is the minimum cost? Page: 4 ot 5 Words: 405 12:41 PM O Type here to search

Explanation / Answer

Given cost function C(x) =0.2x2-6x+8

x- tons of mineral mined.

We have to find x such that total cost will be minimum.

C(x) wil be minimum in a quadratic equation ax2+bx+c where, a >0 is

at x = -b/2a

So, here x = -(-6)/(2*0.2)

x = 15 tons.

Subsituting the x value in the quadratic equation gives us,

C(15) = 0.2(15)2-6(15)+8

= 45-90+8 = -37

So, Minimum of C(x) at x = 15 is -37

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