Homework: HOMEWORK # 3 Score: 0 of 1 pt Bus Econ 2.6.5 22 of 40 (31 complete) Pi

Question

Homework: HOMEWORK # 3 Score: 0 of 1 pt Bus Econ 2.6.5 22 of 40 (31 complete) Pierce Manufacturing determines that the daily revenue n dollars, from the sale of x lawn chairs is R(x)= 0.004x® + 0.02x2 + 0.6x. Currently, Pierce sells 50 lawn chairs daily a) What is the current daily revenue? b) How much would revenue increase if 52 lawn chairs were sold each day? c) What is the marginal revenue when 50 lawn chairs are sold daily? d) Use the answer from part (c) to estimate R(51), R(52), and R(53) a) The current revenue is $

Explanation / Answer

given revenue R(x)=0.004x3+0.02x2+0.6x

=> R'(x)=0.004*3x3-1+0.02*2x2-1+0.6*1

=> R'(x)=0.012x2+0.04x+0.6

(a)

current daily revenue =R(50)

=>current daily revenue =0.004(50)3+0.02(50)2+0.6(50)

=>current daily revenue =$ 580

(b)

increase in revenue =R(52)-R(50)

=>increase in revenue =(0.004(52)3+0.02(52)2+0.6(52))-(0.004(50)3+0.02(50)2+0.6(50))

=>increase in revenue =647.712-580

=>increase in revenue =$ 67.712 exactly

(c)

marginal revenue =R'(50)

=>marginal revenue =0.012(50)2+0.04(50)+0.6

=>marginal revenue =$ 32.6 per chair

(d)

R(51) =R(50) +[(R'(50))(51-50)]

=>R(51) =580+(32.6*(51-50))

=>R(51) =580+32.6

=>R(51) =$ 612.6

R(52) =R(50) +[(R'(50))(52-50)]

=>R(52) =580+(32.6*(52-50))

=>R(52) =580+65.2

=>R(52) =$ 645.2

R(53) =R(50) +[(R'(50))(53-50)]

=>R(53) =580+(32.6*(53-50))

=>R(53) =580+97.8

=>R(53) =$ 677.8

PLEASE RATE IF HELPFUL.PLEASE COMMENT IF YOU HAVE ANY DOUBT

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