Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.11 - Solving Equations and Inequalities Graphically - 1.11 Exercises - Page 122: 47

Answer

$(a)$ See the image below. $(b)$ More than $100$ (At least $101$) $(c)$ $x ∈ (279.13, 400)$ Between the range $(280, 400)$

Work Step by Step

$(a)$ See the image above. $(b)$ As we can see from the graph above, profit becomes positive after $100^{th}$ cooktop. So they gain profit from $101^{st}$. They have to produce more than $100$ (At least $101$). $(c)$ We have to solve the inequality that is: $10x+0.5x^2-0.001x^3-5000>15000$ So, we need region, where the graph is above $y=15000$ line. $x ∈ (279.13, 400)$ As the amount of cooktops should be whole number, we have the range between $(280, 400)$
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