An Aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars and each airplane engine) depends on a number of engines made. If x engines are made, then the unit cost is given by the function C(x)=0.5 X² -280 X + 52506. What is the minimum unit cost?

To find the minimum unit cost, we need to find the vertex of the quadratic function C(x) = 0.5x^2 - 280x + 52506. The x-coordinate of the vertex is given by the formula x = -b/2a, where a and b are the coefficients in the quadratic equation.

In this case, a = 0.5 and b = -280.

Using the formula, x = -(-280)/(2 * 0.5) = 280/1 = 280.

To find the minimum unit cost, substitute the x-coordinate of the vertex (x = 280) into the quadratic function:

C(x) = 0.5(280)^2 - 280(280) + 52506
= 0.5 * 78400 - 78400 + 52506
= 39200 - 78400 + 52506
= 13306.

Therefore, the minimum unit cost is $13,306.

To find the minimum unit cost, we need to determine the value of x that corresponds to the minimum point on the graph of the cost function. In this case, the cost function is given by C(x) = 0.5x² - 280x + 52506.

To find the minimum point, we can start by finding the x-coordinate of the vertex of the quadratic function. The x-coordinate of the vertex is given by the formula: x = -b/2a, where a = 0.5 and b = -280.

Plugging in the values, we have:
x = -(-280)/(2*0.5)
x = 280/1
x = 280

Therefore, the number of engines that need to be made to achieve the minimum cost is 280.

To find the minimum unit cost, we need to substitute this value of x into the cost function C(x):
C(280) = 0.5(280)² - 280(280) + 52506

Calculating this expression, we get:
C(280) = 39,200 - 78,400 + 52,506
C(280) = 13,306

Hence, the minimum unit cost of manufacturing an airplane engine is $13,306.

I still don't understand how to slove it. -

An aircraft factory manufactures airplane engines. The unit cost (the cost in dollars to make each airplane engine) depends on the number of engines made. If engines are made, then the unit cost is given by the function C(x)=1.1x^2-638x_101,067. What is the minimum unit cost?

you notice that C's graph is just a parabola, so its minimum is at the vertex, when x = -b/2a = 280

Don't forget your Algebra I after you've gone on to more advanced topics.