Other Math

0/1 pts Incorrect Question 4 Constraints often take the form of an expression involving one or more decision variables being or < some value. Such values are also called: Objective Coefficients Y-Intercepts Right Hand Sides Ranges of Feasibility Question8 0/ 1 pts Consider this LP Formulation: Let: M = # of Manual gearboxes A-# of Automatic gearboxes Maximize Proft: 64M+100A Subject to: 3M+5A7500 5M+4A 10000 The values 7500 and 1000 are: right hand sides the range of feasibility decision variables objective function

EXPERT ANSWER (1) The values will lie on the right-hand side of the constraint inequalities. Answer: Right hand sides (2) The values which lie on the right-hand sides are simply called right hand sides Answer: Right hand sides

1. (15 marks) Please see the picture on the next page. The yellow cells are for data; each green cell needs to contain a formula to calculate something. Make an Excel worksheet, putting your name and student number in cell F1. Enter labels as shown into the white cells, and the numbers as shown into the yellow cells, but do not enter the numbers into the green cells. NII the formulas must reference cells; do not embed the data from the yellow cells into the formulas in the green cells. If after doing parts (i), (ii), and (iii), you have put the correct formulas into the green cells, then the numbers will match those shown on the next page. In terms of difficulty. part (i) is casy, part (ii) is medium, and part (iii) is hard. (i) ( 2 marks) Λ Department of Highways wishes to construct a straight road from a point at location ( X 1 ​ ,Y 1 ​ ) (metres cast and north of a standard reference point) in cells A6 and B6 to a point at location (X 2 ​ ,Y 2 ​ ) in cells C6 and D6 . Write the Excel formula to be placed in cell F.6 which calculates the Euclidean distance. (ii) (4 marks) Each student’s record consists of a project, two midterm tests, and a final exam. All these marks are out of 100. The overall mark is based on 10% for the project, 20% for each midterm, and 50% for the final cxam. There is data for three students. Write a formula for cell F 10 to be copied into F10:F12 which computes each mark and rounds it to the nearest integer. Notwithstanding this, a student whose overall mark is <50 but whose mark in the final exam is at least 50 will obtain a final mark of 50 . Write a formula for cell G10 to be copied to G10:G12 which computes each potentially adjusted mark (and leaves it unchangcd otherwisc). (iii) ( 6 marks) For each individual, a country has no income tax payable on the first $10,000 of income, a tax of 20% on the next $40,000 of income, a tax of 35% on the next $50,000 of income, and a tax of 50% on all additional income. For example, the income tax payable by a person who makes $120,000 per year would be: 0%($10,000)+20%($40000)+35%($50,000)+50%($20,000)=$35,500. There are four persons, whose income is in the range D17:D20. Using a nested IF or an IFS function, write the Excel formula for cell F17 to be copied to F17:F20 which computes the income tax for these four individuals. (a) (3 marks) With your name and student number on it, submit the file in normal (numerical) view. (b) ((i)2+(ii)4+( iii )6=12 marks) Either submit at least columns. F and G in formula view (with these columns wide cnough to see all formulas), or in Word or pdf write out the formulas used for cells F6, F10, G10, and F17.

EXPERT ANSWER i. The general formula for Euclidean distance between the given points is The excel formula for this in the cell F6 is =SQRT((C6-A6)^2+(D6-B6)^2) _________________ ii. Below is the formula for F10 to F12 and G10 to G12. In Excel, the formula can be entered in F10 & G10 and then copy-pasted into the remaining …

1. (15 marks) Please see the picture on the next page. The yellow cells are for data; each green cell needs to contain a formula to calculate something. Make an Excel worksheet, putting your name and student number in cell F1. Enter labels as shown into the white cells, and the numbers as shown into the yellow cells, but do not enter the numbers into the green cells. NII the formulas must reference cells; do not embed the data from the yellow cells into the formulas in the green cells. If after doing parts (i), (ii), and (iii), you have put the correct formulas into the green cells, then the numbers will match those shown on the next page. In terms of difficulty. part (i) is casy, part (ii) is medium, and part (iii) is hard. (i) ( 2 marks) Λ Department of Highways wishes to construct a straight road from a point at location ( X 1 ​ ,Y 1 ​ ) (metres cast and north of a standard reference point) in cells A6 and B6 to a point at location (X 2 ​ ,Y 2 ​ ) in cells C6 and D6 . Write the Excel formula to be placed in cell F.6 which calculates the Euclidean distance. (ii) (4 marks) Each student’s record consists of a project, two midterm tests, and a final exam. All these marks are out of 100. The overall mark is based on 10% for the project, 20% for each midterm, and 50% for the final cxam. There is data for three students. Write a formula for cell F 10 to be copied into F10:F12 which computes each mark and rounds it to the nearest integer. Notwithstanding this, a student whose overall mark is <50 but whose mark in the final exam is at least 50 will obtain a final mark of 50 . Write a formula for cell G10 to be copied to G10:G12 which computes each potentially adjusted mark (and leaves it unchangcd otherwisc). (iii) ( 6 marks) For each individual, a country has no income tax payable on the first $10,000 of income, a tax of 20% on the next $40,000 of income, a tax of 35% on the next $50,000 of income, and a tax of 50% on all additional income. For example, the income tax payable by a person who makes $120,000 per year would be: 0%($10,000)+20%($40000)+35%($50,000)+50%($20,000)=$35,500. There are four persons, whose income is in the range D17:D20. Using a nested IF or an IFS function, write the Excel formula for cell F17 to be copied to F17:F20 which computes the income tax for these four individuals. (a) (3 marks) With your name and student number on it, submit the file in normal (numerical) view. (b) ((i)2+(ii)4+( iii )6=12 marks) Either submit at least columns. F and G in formula view (with these columns wide cnough to see all formulas), or in Word or pdf write out the formulas used for cells F6, F10, G10, and F17. Read More »

Let be a rational preference relation on X. Then the following hold: (a) The strict relation > is irreflexive and transitive. (b) The indifference relation is reflexive, symmetric, and transitive. (C) If x > y and yz, then x > z.

EXPERT ANSWER Ans. a. The preference relation ≻ is irreflexive and transitive. Let there are two commodity bundles x and y X ≻ Y implies that the relation ≻ is transitive. Similarly if Y ≻ X then also it is transitive. Now, X≻ X is anti-reflexive. X cannot be preferred to X. X is thus …

Let be a rational preference relation on X. Then the following hold: (a) The strict relation > is irreflexive and transitive. (b) The indifference relation is reflexive, symmetric, and transitive. (C) If x > y and yz, then x > z. Read More »

A lash adjuster keeps the pressure constant on engine valves, increasing automobile engines’ fuel efficiency. The relationship between price (p) and monthly demand (D) for lash adjusters made by the Wicks Company is given by this equation: D=(2,000− p)/0.20. a) What is the demand (D) when total revenue is maximized? b) What important data are needed if maximum profit is desired?

EXPERT ANSWER D= (2000 – P) / 0.20 D =? To maximize total revenue. You should use D = a / 2b Note that you should convert the demand function to price function before doing the calculation . P = 2000 – 0.2 D D = 2000 / 2×0.2 = 5000 units Variable cost is …

A lash adjuster keeps the pressure constant on engine valves, increasing automobile engines’ fuel efficiency. The relationship between price (p) and monthly demand (D) for lash adjusters made by the Wicks Company is given by this equation: D=(2,000− p)/0.20. a) What is the demand (D) when total revenue is maximized? b) What important data are needed if maximum profit is desired? Read More »

You have to color a planar map using only four colors, in such a way that no two adjacent regions have the same color.

Give a complete problem formulation for each of the following. You have to color a planar map using only four colors, in such a way that no two adjacent regions have the same color. A 3-foot-tall monkey is in a room where some bananas are suspended from the 8-foot ceiling. He would like to get …

You have to color a planar map using only four colors, in such a way that no two adjacent regions have the same color. Read More »