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A manufacturer of lighting fixtures has daily production costs of $ C = 800 - 10x + 0.25x^2 $, where $ C $ is the total cost (in dollars) and $ x $ is the number of units produced. How many fixtures should be produced each day to yield a minimum cost?

20

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Titus K.

July 30, 2021

) A manufacturing firm finds that the daily costs of producing x units of a product is given by: ???? = ????. ???????????????? ???? + ???????????? + ???????????? a. If each of the units is sold for Ksh 20, determine the minimum numbers that must be prod

If the selling price is increased by 45%, at what level of production would the company not incur any losses?

McMaster University

University of Michigan - Ann Arbor

Idaho State University

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so the daily production costs see is given by the following expression the quadratic where X is the number of units that are produced in the given day. So notice here if we don't have to give a precise graph of C, but it's important to notice that since the leading coefficient is positive number, this is a problem that opens up work so more or less we have something like this and what we're trying to his minimize cost. We're trying to minimize the see value, and that means that we want the Vertex. So the vortex will give us some point h k or case the minimum cost. And then this is the corresponding X value which gives the minimum cost. So we're trying to figure out what value of X should we choose that minimizes the cost of our production. So the X that we should use here is the X coordinate no of the vertex or, if you'd like, you could just call it a tch. But the nice thing about parabolas is that this is always given by the expression in your textbook negative B over two A, where a B and C here from the following. These are the coefficients of Europe Quadratic. So here are our problem. We just need the O and the B. Well, see, that is point two five Be his negative ten. So this gives us negative negative ten over two times point two five. And if you simplify that and you get twenty so if you want to minimize the cost, you should produce twenty units and one day

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