(A) Explanation Consider x and y as the production of number of tables and chairs per day, respectively. The maximum profit made by the company are $90 and $25 on the production of tables and chairs per day, respectively. Then the maximum function is P = 90 x + 25 y . The department of assembly needs 8 tables and 2 chairs for the maximum labor-hours of 400 per day, respectively. That is, 8 x + 2 y ≤ 400 . The department of finishing needs 2 tables and a chair for the maximum labor-hours of 120 per day, respectively. That is, 2 x + y ≤ 120 . Now draw the inequalities 8 x + 2 y ≤ 400 and 2 x + y ≤ 120 and plot its corner points as shown in below Figure 1. From Figure 1, the shaded region is the solution set for the inequalities 8 x + 2 y ≤ 400 and 2 x + y ≤ 120 for x , y ≥ 0 . Thus, the corner points on the feasible regions are ( 0 , 0 ) , ( 0 , 120 ) , ( 40 , 40 ) and ( 50 , 0 ) . Now list out the maximum profit function of P = 90 x + 25 y for the given corner points as shown in below table 1 (B) To determine To discuss: The effect on the production schedule of the maximum profit if the government restrict the emission of sulfur dioxide to 11,500 grams.

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

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Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Chapter 5.3, Problem 50E

(A)

To determine

Number of tables and chairs needs to be manufactured to meet the daily maximum profit and the maximum profit.

(B)

To determine

To discuss: The effect on the production schedule of the maximum profit if the government restrict the emission of sulfur dioxide to 11,500 grams.

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Chapter 5.3, Problem 49E

Chapter 5.3, Problem 51E

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An improved method that is similar to Euler's method is what is usually called the Improved Euler's method. It works like this: Consider an equation y' = f(x, y). From (xn, Yn), our approximation to the solution of the differential equation at the n-th stage, we find the next stage by computing the x-step Xn+1 = xn +h, and then k1, the slope at (xn, Yn). The predicted new value of the solution . İs Zn+1 = Yn + h · k₁. Then we find the slope at the predicted new point k₁ = f(xn+1, Zn+1) and get the corrected point by averaging slopes h Yn+1 = = Yn + 1½ ½ (k1 + k₂). Suppose that we use the Improved Euler's method to approximate the solution to the differential equation dy dx = x - 0.5y, y(0.5) = 9. We let xo = 0.5 and yo 9 and pick a step size h = 0.25. Complete the following table: n xn Yn k1 Zn+1 k₂ 0 0.59-48 -3.25 ♡ <+ help (numbers) The exact solution can also be found for the linear equation. Write the answer as a function of x. y(x) = = help (formulas) Thus the actual value of the…

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Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

Ch. 5.1 - Graph 6x − 3y > 18. Ch. 5.1 - Prob. 2MP Ch. 5.1 - Prob. 3MP Ch. 5.1 - Prob. 4MP Ch. 5.1 - Prob. 1ED Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E

Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Graph each inequality in Problems 9–18. 14. y < 5 Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - In Problems 19–22, graph the set of points that...Ch. 5.1 - Prob. 20E Ch. 5.1 - In Problems 19-22, graph the set of points that...Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - In Problems 23–32, define the variable and...Ch. 5.1 - In Problems 23–32, define the variable and...Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - In Exercises 33–38, state the linear inequality...Ch. 5.1 - In Exercises 33–38, state the linear inequality...Ch. 5.1 - In Exercises 33–38, state the linear inequality...Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - In Problems 39–44, define two variables and...Ch. 5.1 - In Problems 39–44, define two variables and...Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - In Problems 39–44, define two variables and...Ch. 5.1 - In Problems 45–54, graph each inequality subject...Ch. 5.1 - Prob. 46E Ch. 5.1 - In Problems 45–54, graph each inequality subject...Ch. 5.1 - Prob. 48E Ch. 5.1 - In Problems 45–54, graph each inequality subject...Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Applications In Problems 55–66, express your...Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.1 - Prob. 59E Ch. 5.1 - Prob. 60E Ch. 5.1 - Prob. 61E Ch. 5.1 - Prob. 62E Ch. 5.1 - Prob. 63E Ch. 5.1 - Prob. 64E Ch. 5.1 - Prob. 65E Ch. 5.1 - Prob. 66E Ch. 5.2 - Matched Problem 1 Solve the following system of...Ch. 5.2 - Prob. 2MP Ch. 5.2 - Prob. 3MP Ch. 5.2 - Prob. 1ED Ch. 5.2 - Prob. 1E Ch. 5.2 - Prob. 2E Ch. 5.2 - Prob. 3E Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - Prob. 6E Ch. 5.2 - Prob. 7E Ch. 5.2 - Prob. 8E Ch. 5.2 - In Problems 9–12, match the solution region of...Ch. 5.2 - Prob. 10E Ch. 5.2 - Prob. 11E Ch. 5.2 - Prob. 12E Ch. 5.2 - Prob. 13E Ch. 5.2 - Prob. 14E Ch. 5.2 - Prob. 15E Ch. 5.2 - Prob. 16E Ch. 5.2 - In Problems 17–20, match the solution region of...Ch. 5.2 - Prob. 18E Ch. 5.2 - In Problems 17–20, match the solution region of...Ch. 5.2 - Prob. 20E Ch. 5.2 - Prob. 21E Ch. 5.2 - Prob. 22E Ch. 5.2 - Prob. 23E Ch. 5.2 - Prob. 24E Ch. 5.2 - Prob. 25E Ch. 5.2 - Prob. 26E Ch. 5.2 - Prob. 27E Ch. 5.2 - Prob. 28E Ch. 5.2 - Prob. 29E Ch. 5.2 - Prob. 30E Ch. 5.2 - Prob. 31E Ch. 5.2 - Prob. 32E Ch. 5.2 - Prob. 33E Ch. 5.2 - Prob. 34E Ch. 5.2 - Prob. 35E Ch. 5.2 - Prob. 36E Ch. 5.2 - Prob. 37E Ch. 5.2 - Prob. 38E Ch. 5.2 - Prob. 39E Ch. 5.2 - Prob. 40E Ch. 5.2 - Prob. 41E Ch. 5.2 - Prob. 42E Ch. 5.2 - Prob. 43E Ch. 5.2 - Prob. 44E Ch. 5.2 - Prob. 45E Ch. 5.2 - Prob. 46E Ch. 5.2 - Prob. 47E Ch. 5.2 - Prob. 48E Ch. 5.2 - Prob. 49E Ch. 5.2 - Prob. 50E Ch. 5.2 - Prob. 51E Ch. 5.2 - Prob. 52E Ch. 5.2 - Water skis. Refer to Problem 51. The company...Ch. 5.2 - Prob. 54E Ch. 5.2 - Prob. 55E Ch. 5.2 - Prob. 56E Ch. 5.2 - Psychology. A psychologist uses two types of boxes...Ch. 5.3 - A manufacturing plant makes two types of...Ch. 5.3 - Prob. 2MP Ch. 5.3 - Prob. 3MP Ch. 5.3 - Prob. 1ED Ch. 5.3 - Prob. 2ED Ch. 5.3 - Prob. 1E Ch. 5.3 - Prob. 2E Ch. 5.3 - Prob. 3E Ch. 5.3 - Prob. 4E Ch. 5.3 - Prob. 5E Ch. 5.3 - Prob. 6E Ch. 5.3 - Prob. 7E Ch. 5.3 - Prob. 8E Ch. 5.3 - Prob. 9E Ch. 5.3 - Prob. 10E Ch. 5.3 - Prob. 11E Ch. 5.3 - Prob. 12E Ch. 5.3 - Prob. 13E Ch. 5.3 - Prob. 14E Ch. 5.3 - Prob. 15E Ch. 5.3 - Prob. 16E Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Prob. 18E Ch. 5.3 - Prob. 19E Ch. 5.3 - Prob. 20E Ch. 5.3 - Prob. 21E Ch. 5.3 - Prob. 22E Ch. 5.3 - Prob. 23E Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Prob. 25E Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Prob. 27E Ch. 5.3 - Prob. 28E Ch. 5.3 - Prob. 29E Ch. 5.3 - Prob. 30E Ch. 5.3 - Prob. 31E Ch. 5.3 - Prob. 32E Ch. 5.3 - Prob. 33E Ch. 5.3 - Prob. 34E Ch. 5.3 - Prob. 35E Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Prob. 37E Ch. 5.3 - Prob. 38E Ch. 5.3 - In Problems 39 and 40, explain why Theorem 2...Ch. 5.3 - In Problems 39 and 40, explain why Theorem 2...Ch. 5.3 - Prob. 41E Ch. 5.3 - Prob. 42E Ch. 5.3 - Prob. 43E Ch. 5.3 - Prob. 44E Ch. 5.3 - Prob. 45E Ch. 5.3 - Prob. 46E Ch. 5.3 - Prob. 47E Ch. 5.3 - Problems 41–48 refer to the bounded feasible...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - Prob. 50E Ch. 5.3 - In Problems 49–64, construct a mathematical model...Ch. 5.3 - Prob. 52E Ch. 5.3 - In Problems 49–64, construct a mathematical model...Ch. 5.3 - Prob. 54E Ch. 5.3 - In Problems 49–64, construct a mathematical model...Ch. 5.3 - Prob. 56E Ch. 5.3 - Prob. 57E Ch. 5.3 - Prob. 58E Ch. 5.3 - Prob. 59E Ch. 5.3 - Prob. 60E Ch. 5.3 - Prob. 61E Ch. 5.3 - Prob. 62E Ch. 5.3 - Psychology. A psychologist uses two types of boxes...Ch. 5.3 - Sociology. A city council voted to conduct a study...Ch. 5 - Prob. 1RE Ch. 5 - Prob. 2RE Ch. 5 - Prob. 3RE Ch. 5 - Prob. 4RE Ch. 5 - Prob. 5RE Ch. 5 - Prob. 6RE Ch. 5 - Prob. 7RE Ch. 5 - Prob. 8RE Ch. 5 - Prob. 9RE Ch. 5 - Prob. 10RE Ch. 5 - Prob. 11RE Ch. 5 - Prob. 12RE Ch. 5 - Prob. 13RE Ch. 5 - Prob. 14RE Ch. 5 - In Problems 15 and 16, construct a mathematical...Ch. 5 - Prob. 16RE

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