Asked by Sinachi
The total cost, y naira, manufacturing x units of an article is given by the relation y=(5/4)x^2+20/x. Find the number of units of the articles for which the cost of manufacture is least and the corresponding least cost
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To find the number of units of the article for which the cost of manufacture is least, we need to minimize the cost function y.
To do this, we'll take the derivative of y with respect to x and set it equal to zero:
dy/dx = (5/4)(2x) - 20/x^2 = (10/4)x - 20/x^2 = (5/2)x - 20/x^2
Setting this equal to zero and solving for x:
(5/2)x - 20/x^2 = 0
(5/2)x = 20/x^2
(x^3)(5/2) = 20
5x^3 = 40
x^3 = 8
x = 2
So the number of units of the article for which the cost of manufacture is least is 2.
To find the corresponding least cost, we substitute x = 2 into the cost function y:
y = (5/4)(2^2) + 20/(2)
y = (5/4)(4) + 10
y = 5 + 10
y = 15
Therefore, the number of units of the articles for which the cost of manufacture is least is 2, and the corresponding least cost is 15 naira.
To do this, we'll take the derivative of y with respect to x and set it equal to zero:
dy/dx = (5/4)(2x) - 20/x^2 = (10/4)x - 20/x^2 = (5/2)x - 20/x^2
Setting this equal to zero and solving for x:
(5/2)x - 20/x^2 = 0
(5/2)x = 20/x^2
(x^3)(5/2) = 20
5x^3 = 40
x^3 = 8
x = 2
So the number of units of the article for which the cost of manufacture is least is 2.
To find the corresponding least cost, we substitute x = 2 into the cost function y:
y = (5/4)(2^2) + 20/(2)
y = (5/4)(4) + 10
y = 5 + 10
y = 15
Therefore, the number of units of the articles for which the cost of manufacture is least is 2, and the corresponding least cost is 15 naira.
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