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The total cost N(x) in rupees, associated with the production of x units of an item is given by N(x)=0.06x3-0.01x2+10x-43. Find the marginal cost when 5 units are produced.
- a)Rs. 1.44
- b)Rs. 144.00
- c)Rs. 14.4
- d)Rs. 56.2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The total cost N(x) in rupees, associated with the production of x uni...
Given, N(x) = 0.06x^3 - 0.01x^2 + 10x - 43
Marginal Cost (MC) is the derivative of the total cost function with respect to the number of units produced i.e.
MC = dN(x)/dx
To find the marginal cost when 5 units are produced, we need to find the derivative of the total cost function and substitute x=5.
N(x) = 0.06x^3 - 0.01x^2 + 10x - 43
dN(x)/dx = 0.18x^2 - 0.02x + 10
Substituting x=5,
MC = dN(x)/dx at x=5
MC = 0.18(5)^2 - 0.02(5) + 10
MC = 1.44
Therefore, the marginal cost when 5 units are produced is Rs. 144.00, which is option (b).
Marginal Cost (MC) is the derivative of the total cost function with respect to the number of units produced i.e.
MC = dN(x)/dx
To find the marginal cost when 5 units are produced, we need to find the derivative of the total cost function and substitute x=5.
N(x) = 0.06x^3 - 0.01x^2 + 10x - 43
dN(x)/dx = 0.18x^2 - 0.02x + 10
Substituting x=5,
MC = dN(x)/dx at x=5
MC = 0.18(5)^2 - 0.02(5) + 10
MC = 1.44
Therefore, the marginal cost when 5 units are produced is Rs. 144.00, which is option (b).
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Community Answer
The total cost N(x) in rupees, associated with the production of x uni...
The marginal cost is given by the rate of change of revenue.
Hence, (dN(x)/dt) =0.18x2-0.02x+10.
∴
= 0.18(5)2-0.02(5)+10
= 4.5-0.1+10
= Rs. 14.4
Hence, (dN(x)/dt) =0.18x2-0.02x+10.
∴
= 0.18(5)2-0.02(5)+10= 4.5-0.1+10
= Rs. 14.4
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The total cost N(x) in rupees, associated with the production of x units of an item is given by N(x)=0.06x3-0.01x2+10x-43. Find the marginal cost when 5 units are produced.a)Rs. 1.44b)Rs. 144.00c)Rs. 14.4d)Rs. 56.2Correct answer is option 'B'. Can you explain this answer?
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