Finite Mathematics & Its Applications (12th Edition)
12th Edition
ISBN: 9780134437767
Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair
Publisher: PEARSON
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Textbook Question
Chapter 3.3, Problem 38E
Refining A refinery has two smelters that extract metallic iron from iron ore. Smelter A processes 1000 tons of iron ore per hour and uses 7 megawatts of energy per hour. Smelter B processes 2000 tons of iron ore per hour and uses 13 megawatts of energy per hour. Each refinery must be operated at least 8 hours per day and, of course, no more than 24 hours. If the refinery must process at least 30,000 tons of iron ore per day, how many hours should each smelter operate in order to expend as little energy as possible?
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Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.
By considering appropriate series expansions,
ex · ex²/2 . ¸²³/³ . . ..
=
= 1 + x + x² +……
when |x| < 1.
By expanding each individual exponential term on the left-hand side
and multiplying out, show that the coefficient of x 19 has the form
1/19!+1/19+r/s,
where 19 does not divide s.
Let
1
1
r
1+
+ +
2 3
+
=
823
823s
Without calculating the left-hand side, prove that r = s (mod 823³).
Chapter 3 Solutions
Finite Mathematics & Its Applications (12th Edition)
Ch. 3.1 - Graph the inequality 3xy3.Ch. 3.1 - Graph the feasible set for the system of...Ch. 3.1 - In Exercises 1-4, state whether the inequality is...Ch. 3.1 - In Exercises 1-4, state whether the inequality is...Ch. 3.1 - In Exercises 1-4, state whether the inequality is...Ch. 3.1 - In Exercises 1-4, state whether the inequality is...Ch. 3.1 - In Exercises 5-7, solve for x, 2x53Ch. 3.1 - Prob. 6ECh. 3.1 - In Exercises 5-7, solve for x,
7.
Ch. 3.1 - Which of the following results from solving x+13...
Ch. 3.1 - Prob. 9ECh. 3.1 - In Exercises 9-14, write the linear inequality in...Ch. 3.1 - In Exercises 9-14, write the linear inequality in...Ch. 3.1 - In Exercises 9-14, write the linear inequality in...Ch. 3.1 - In Exercises 9-14, write the linear inequality in...Ch. 3.1 - In Exercises 9-14, write the linear inequality in...Ch. 3.1 - In Exercises 15-22, determine whether or not the...Ch. 3.1 - In Exercises 15-22, determine whether or not the...Ch. 3.1 - In Exercises 15-22, determine whether or not the...Ch. 3.1 - In Exercises 15-22, determine whether or not the...Ch. 3.1 - In Exercises 15-22, determine whether or not the...Ch. 3.1 - In Exercises 15-22, determine whether or not the...Ch. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - In Exercises 23-26, graph the given inequality by...Ch. 3.1 - In Exercises 23-26, graph the given inequality by...Ch. 3.1 - Prob. 25ECh. 3.1 - In Exercises 23-26, graph the given inequality by...Ch. 3.1 - In Exercises 27-30, give the linear inequality...Ch. 3.1 - In Exercises 27-30, give the linear inequality...Ch. 3.1 - In Exercises 27-30, give the linear inequality...Ch. 3.1 - In Exercises 27-30, give the linear inequality...Ch. 3.1 - In Exercises 31-42, graph the given inequality....Ch. 3.1 - In Exercises 31-42, graph the given...Ch. 3.1 - In Exercises 31-42, graph the given inequality. x2Ch. 3.1 - In Exercises 31-42, graph the given inequality. x0Ch. 3.1 - In Exercises 31-42, graph the given...Ch. 3.1 - In Exercises 31-42, graph the given inequality....Ch. 3.1 - In Exercises 31-42, graph the given inequality....Ch. 3.1 - In Exercises 31-42, graph the given...Ch. 3.1 - In Exercises 31-42, graph the given inequality....Ch. 3.1 - In Exercises 31-42, graph the given...Ch. 3.1 - In Exercises 31-42, graph the given inequality....Ch. 3.1 - In Exercises 31-42, graph the given inequality....Ch. 3.1 - In Exercises 43-48, graph the feasible set for the...Ch. 3.1 - In Exercises 43-48, graph the feasible set for the...Ch. 3.1 - In Exercises 43-48, graph the feasible set for the...Ch. 3.1 - In Exercises 43-48, graph the feasible set for the...Ch. 3.1 - In Exercises 43-48, graph the feasible set for the...Ch. 3.1 - In Exercises 43-48, graph the feasible set for the...Ch. 3.1 - In Exercises 49-52, determine whether the given...Ch. 3.1 - In Exercises 49-52, determine whether the given...Ch. 3.1 - In Exercises 49-52, determine whether the given...Ch. 3.1 - In Exercises 49-52, determine whether the given...Ch. 3.1 - In Exercises 52-56, determine whether the given...Ch. 3.1 - In Exercises 52-56, determine whether the given...Ch. 3.1 - In Exercises 52-56, determine whether the given...Ch. 3.1 - In Exercises 52-56, determine whether the given...Ch. 3.1 - Give a system of inequalities for which the graph...Ch. 3.1 - The shaded region in Fig. 9 is bounded by four...Ch. 3.1 - The shaded region in Fig. 10 is bounded by four...Ch. 3.1 - Which quadrant if Fig. 11 contains no points that...Ch. 3.1 - Graph the line 4x2y=7. (a) Locate the point on the...Ch. 3.1 - 62. Graph the line
(a) Locate the point on the...Ch. 3.1 - Display the feasible set in Exercise 47.Ch. 3.1 - Display the feasible set in Exercise 48.Ch. 3.2 - 1. Determine whether the following points are in...Ch. 3.2 - A physical fitness enthusiast decides to devote...Ch. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - In Exercises 14, determine whether the given point...Ch. 3.2 - Prob. 4ECh. 3.2 - Manufacturing Consider the furniture manufacturing...Ch. 3.2 - 6. Manufacturing Consider the furniture...Ch. 3.2 - Packaging Joes Confectionary puts together two...Ch. 3.2 - Nutrition-Animal Mr. Holloway decides to feed his...Ch. 3.2 - Shipping A truck traveling from New York to...Ch. 3.2 - 10. Mining A coal company owns mines in two...Ch. 3.2 - 11. Exam Strategy A student is taking an exam...Ch. 3.2 - 12. Political Campaign—Resource Allocation A local...Ch. 3.2 - Nutrition-Dairy Cows A dairy farmer concludes that...Ch. 3.2 - Manufacturing-Resource Allocation A clothing...Ch. 3.3 - The feasible set for the nutrition problem of...Ch. 3.3 - 2. Rework the nutrition problem, assuming that...Ch. 3.3 - For each of the feasible sets in Exercises 1–4,...Ch. 3.3 - For each of the feasible sets in Exercises 14,...Ch. 3.3 - For each of the feasible sets in Exercises 14,...Ch. 3.3 - Prob. 4ECh. 3.3 - In Exercises 58, find the values of x and y that...Ch. 3.3 - In Exercises 58, find the values of x and y that...Ch. 3.3 - In Exercises 58, find the values of x and y that...Ch. 3.3 - In Exercises 5–8, find the values of x and y that...Ch. 3.3 - In Exercises 9–12, find the values of x and y that...Ch. 3.3 - In Exercises 9–12, find the values of x and y that...Ch. 3.3 - In Exercises 9–12, find the values of x and y that...Ch. 3.3 - In Exercises 9–12, find the values of x and y that...Ch. 3.3 - 13. Nutrition—People Consider the nutrition...Ch. 3.3 - 14. Nutrition—People Consider the nutrition...Ch. 3.3 - 15. Packaging Refer to Exercises 3.2, Problem 7....Ch. 3.3 - Nutrition-Animal Refer to Exercises 3.2, Problem...Ch. 3.3 - 17. Shipping Refer to Exercises 3.2, Problem 9....Ch. 3.3 - 18. Mining Refer to Exercises 3.2, Problem 10....Ch. 3.3 - Exam Strategy Refer to Exercises 3.2, Problem 11....Ch. 3.3 - Political Campaign-Resource Allocation Refer to...Ch. 3.3 - 21. Nutrition—Dairy Cows Refer to Exercises 3.2,...Ch. 3.3 - Manufacturing-Resource Allocation Refer to...Ch. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - In Exercises 25–32, find the optimal value for the...Ch. 3.3 - In Exercises 25–32, find the optimal value for the...Ch. 3.3 - In Exercises 2532, find the optimal value for the...Ch. 3.3 - In Exercises 25–32, find the optimal value for the...Ch. 3.3 - In Exercises 25–32, find the optimal value for the...Ch. 3.3 - In Exercises 25–32, find the optimal value for the...Ch. 3.3 - In Exercises 2532, find the optimal value for the...Ch. 3.3 - In Exercises 25–32, find the optimal value for the...Ch. 3.3 - 33. Manufacturing—Resource Allocation Infotron,...Ch. 3.3 - 34. Manufacturing—Production Planning An...Ch. 3.3 - Agriculture-Crop Planning A farmer has 100 acres...Ch. 3.3 - 36. Manufacturing—Resource Allocation A company...Ch. 3.3 - 37. Manufacturing The E-JEM Company produces two...Ch. 3.3 - Refining A refinery has two smelters that extract...Ch. 3.3 - 39. Nutrition—People A nutritionist, working for...Ch. 3.3 - 40. Construction—Resource Allocation A contractor...Ch. 3.3 - 41. Packaging—Product Mix The Beautiful Day Fruit...Ch. 3.3 - 42. Manufacturing—Resource Allocation The Bluejay...Ch. 3.3 - Agriculture-Crop Planning Suppose that the farmer...Ch. 3.3 - 44. Nutrition Pavan wants to add a sliced carrot...Ch. 3.3 - Packaging A small candy shop makes a special Cupid...Ch. 3.3 - Prob. 46ECh. 3.3 - 47. Packaging A bath shop sells two different gift...Ch. 3.3 - Packaging A florist offers two types of Thank You...Ch. 3.3 - Consider the following linear programming problem:...Ch. 3.3 - Consider the following linear programming problem:...Ch. 3.3 - Prob. 51ECh. 3.3 - Use Excel or Wolfram| Alpha to solve Exercise 26.Ch. 3.4 - Problems 1–3 refer to Example 1. Translate the...Ch. 3.4 - Problems 13 refer to Example 1. Translate the...Ch. 3.4 - Problems 13 refer to Example 1. Translate the...Ch. 3.4 - A linear programming problem has objective...Ch. 3.4 - 1. Figure 10(a) shows the feasible set of the...Ch. 3.4 - Figure 10(b) shows the feasible set of the...Ch. 3.4 - Consider the feasible set in Fig. 11, where three...Ch. 3.4 - Consider the feasible set in Fig. 11, where three...Ch. 3.4 - Consider the feasible set in Fig. 11, where three...Ch. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Consider the feasible set in Fig. 12, where three...Ch. 3.4 - Consider the feasible set in Fig. 12, where three...Ch. 3.4 - Consider the feasible set in Fig. 12, where three...Ch. 3.4 - Consider the feasible set in Fig. 13. For what...Ch. 3.4 - Prob. 12ECh. 3.4 - Nutrition-Animal Mr. Smith decides to feed his pet...Ch. 3.4 - Oil Production An oil company owns two refineries....Ch. 3.4 - Investment Planning Mr. Jones has $9000 to invest...Ch. 3.4 - Shipping-Product Mix A produce dealer in Florida...Ch. 3.4 - 17. Transportation—Shipping A foreign-car...Ch. 3.4 - Transportation-Shipping Consider the foreign-car...Ch. 3.4 - Manufacturing-Production Planning An oil refinery...Ch. 3.4 - 20. Manufacturing—Production Planning Suppose that...Ch. 3.4 - 21. Shipping—Resource Allocation A shipping...Ch. 3.4 - Shipping-Resource Allocation Suppose that the...Ch. 3.4 - 23. Transportation—Shipping A major coffee...Ch. 3.4 - Transportation-Shipping Consider the coffee...Ch. 3.4 - 25. Packaging—Product Mix A pet store sells three...Ch. 3.4 - Prob. 26ECh. 3.4 - 27. Refer to Fig. 6. As the lines of constant...Ch. 3.4 - Figure 16 shows the feasible set for the nutrition...Ch. 3.4 - Consider the feasible set in Fig. 17(a). In...Ch. 3.4 - Consider the feasible set in Fig. 17(a). In...Ch. 3.4 - Consider the feasible set in Fig. 17(a). In...Ch. 3.4 - Consider the feasible set in Fig. 17(a). In...Ch. 3.4 - Consider the feasible set in Fig. 17(a). In...Ch. 3.4 - Consider the feasible set in Fig. 17(a). In...Ch. 3.4 - Consider the feasible set in Fig. 17(a). In...Ch. 3.4 - Consider the feasible set in Fig. 17(a). In...Ch. 3.4 - Prob. 37ECh. 3 - State the inequality properties for addition,...Ch. 3 - What are the general forms of a linear inequality...Ch. 3 - Prob. 3FCCECh. 3 - 4. What is meant by the feasible set of a system...Ch. 3 - Prob. 5FCCECh. 3 - Prob. 6FCCECh. 3 - Prob. 7FCCECh. 3 - Prob. 8FCCECh. 3 - 9. Give a procedure for solving a linear...Ch. 3 - Prob. 1RECh. 3 - 2. Graph the linear inequality.
Ch. 3 - 3. Write the inequality whose graph is the...Ch. 3 - 4. Travel—Resource Allocation Terrapin Airlines...Ch. 3 - Nutrition-People A nutritionist is designing a new...Ch. 3 - Prob. 6RECh. 3 - Packaging-Product Mix A confectioner makes two...Ch. 3 - Prob. 8RECh. 3 - Packaging-Resource Allocation A computer company...Ch. 3 - Transportation-Shipping An appliance company has...Ch. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - When mathematicians are presented with a linear...Ch. 3 - When mathematicians are presented with a linear...Ch. 3 - When mathematicians are presented with a linear...Ch. 3 - When mathematicians are presented with a linear...Ch. 3 - When mathematicians are presented with a linear...Ch. 3 - When mathematicians are presented with a linear...
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