Consider the cost function C(x)= 4x. + 18x + 21 (thousand dollars). ) what is th
ID: 2884758 • Letter: C
Question
Consider the cost function C(x)= 4x. + 18x + 21 (thousand dollars). ) what is the marginal cost at production level x#3? ) Use the marginal cost at x #3 to estimate the cost of producing 3.50 units. ) Let R(x)=-x2 + 44x + 45 denote the revenue in thousands of dollars generated from the production of x units, what is the break-even point? (Recall th he break-even point is when the revenue is equal to the cost.) ) Compute and compare the marginal revenue and marginal cost at the break-even point. Should the company increase production beyond the break-ev a)The marginal cost at production level x#3iss b) The cost of producing 350 units is c) The break-even point is whenunits are produced. (Type an integer or a fraction.) o) The company producto increase production past the break even pointExplanation / Answer
given cost C(x) =4x2+18x+21
a)
marginal cost = C'(x)
=>marginal cost = 4*2x +18*1 +0
=>marginal cost = 8x +18
at production level x=3
marginal cost =C'(3)
=>marginal cost = 8*3 +18
=>marginal cost = 24 +18
=>marginal cost = 42
The marginal cost at production level x=3 is $ 42000
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b)
cost of producting 3.50 units = (C'(3))*(3.50-3)
=>cost of producting 3.50 units = 42*(3.50-3)
=>cost of producting 3.50 units = 42*(0.50)
=>cost of producting 3.50 units = 21
The cost of producting 3.50 units is $ 21000
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c)
at break even, C(x)=R(x)
=>4x2+18x+21=-x2+44x+45
=>4x2+18x+21+x2-44x-45=0
=>5x2-26x-24=0
=>5x2-30x+4x-24=0
=>5x(x-6)+4(x-6)=0
=>(x-6)(5x+4)=0
=>x-6=0
=>x=6
The break-even point is when 6 units are produced
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d)
C'(x)=8x+18 ,R'(x)=-2x+44
=>C'(6)=8*6 +18 ,R'(6)=-2*6+44
=>C'(6)=66 ,R'(6)=32
since C'(6)>R'(6)
The company should not increase the production past the break-even point
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