The sales of Sherwin-Williams paint in different regional markets depends on sev

Question

The sales of Sherwin-Williams paint in different regional markets depends on several input variables. One variable that partially drives selling price, which in turn affects sales, is the cost to get the product to market. When other input variables are held constant, sales can be modeled as s(x) = 597.3(0.9214x + 12) thousand gallons when it costs x dollars to get a gallon of paint to market, data from 0 ? x ? 2.

(a) How many gallons of paint are sold when it costs 65 cents for a gallon to reach the market? (Round your answer to three decimal places.)

(b) How quickly are sales changing whenx = 0.65? (Round your answer to three decimal places.)

Explanation / Answer

GIven that

s(x) = 597.3(0.9214x+ 12)

where s refers to the sales

A)For this put x=0.65 as we have to find total number of sales at 65 cents

So

s(x) = 597.3(0.9214x+ 12)

x=0.65

s(x)=597.3(0.9214*0.65+12)=7525.3

B)For this part diffrentiate this equation w.r.t. x

s(x) = 597.3(0.9214x+ 12)

So,

s=597.3(0.9214)=550.35

Hope ur all doubts are clear by this..!!

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