Amanufacturer of lighting fixtures has daily production costs pf c(x)= 800- 10x+ 0.25x^2 , where c is the total cost in dollars and x is the number of units produced. determine how many fixtures should be produced each day to yield minimum cost.

20 fixtures

Step-by-step explanation:

There are two methods to getting the number of fixtures to be produced.

Method 1

Given:

C(x) = 800 - 10x +

Re - arranging the function , we have

C(x) = - 10x + 800

This is a typical quadratic expression , since the coefficient of is positive , it means that the quadratic expression is a parabola that opens upward. We can therefore find the x - coordinate of the  vertex of the parabola to find the number of fixtures that can be produced to yield minimum cost.

The formula for finding the x - coordinate of the vertex is give as

From the expression given , a = 0.25 , b = -10 , substituting into the formula , we have:

x =

x = 10/0.5

x = 20

Therefore , 20 fixtures should be produced each day to yield minimum cost.

METHOD 2

This is the application of differential equation , the question means that we need to find the value of x for which the function is minimum. To do this , we will differentiate the function once with respect to x and equate to zero.

C(x) = - 10x + 800

differentiating once , we have

(x) = 0.5x - 10

setting it to zero , we have

0.5x - 10 = 0

0.5x = 10

x = 10/0.5

x = 20

This means that 20 fixtures should be produced each day to yield minimum cost.

x=4

step-by-step explanation:

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.