The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.

Given:

The cost function is:

where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands.

To find:

The minimum production cost.

Solution:

We have,

It is a quadratic function with positive leading efficient. It means it is an upward parabola and its vertex is the point of minima.

If a quadratic function is , then the vertex of the parabola is:

In the given function, . So,

Putting in the given function to find the minimum production cost.

Therefore, the minimum production cost is 0.5625 million dollars.

The minimum cost is 0.5625.

Step-by-step explanation:

The cost function is

C(x) = 0.28x^2 - 0.7 x + 1

Differentiate with respect to x.

The minimum value is

c = 0.28 x 1.25 x 1.25 - 0.7 x 1.25 + 1

C = 0.4375 - 0.875 + 1

C = 0.5625

step-by-step explanation:

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