IE 456 MATHEMATICAL MODELING AND APPLICATIONS Homework 1 1. [15 points] Consider the following linear programming problem: Min z = 3x12x23x3 Subject to x1+2x2 +x3 14 x1+2x2+4x3 12 x1 x2 +x3 = 2 x3 3 x1; x2 unrestricted (a) [6 points] Reformulate the problem so it is in standard format. (b) [6 points] Reformulate the problem so it is in canonical format. (c) [3 points] Convert the problem into a maximization problem. 2. [20 points] A lathe is used to reduce the diameter of a steel shaft whose length is 36 inches (in.) from 14 in. to 12 in. The speed x1 (in revolutions per minute), the depth feed x2 (in inches per minute), and the length feed x3 (in inches per minute) must be determined. The duration of the cut is given …show more content…
(1: tanks, 2: planes, 3: missile batteries). (a) [12 points] Max x1+ 3x2+ 2x3 (22) s.t. 600; 000x1+2; 000; 000x2+800; 000x3 900; 000; 000 (23) x1 200 (24) x2 200 (25) x2 300 (26) x2 4x3 0 (27) x2+ 2x3 0 (28) x1; x2; x3 0: (29) (22) gives the total utility obtained from the military logistics items to maximize. (23) is the budget constraint that restricts the money to spend on the items. (24) { (26) give the limits on the quantity of tanks and planes to acquire. (27) and (28) ensure the ratio of the tanks and missile batteries are within the given limits. Finally, (29) ensure non-negativity of the quantity of items to buy. (b) [3 points] (23) can be rewritten as: 0:6x1 + 2x2 + 0:8x3
teacher I am required to take into account both dimensions. So this became my goal and tool to use.
6. If an object is 4.5 cm long, what would its length be in mm?
Method: By reading MCWP 6-11 Leading Marines, answer and write an analysis on the objectives given per instruction.
In part two, we use the 5g washer, we pull the string 5 degree away from the center, let go and count the time for 10 period, then the Digital timer will show us the average period, Then we use 10g washer and do the same thing. After that we set the string shorter and do the same thing again.
13. Use the ruler to measure the length, width, and height of the magnet in centimeters. Record the measurements in Data Table 5.
1. SITUATION: The Battalion will direct an Army Personnel Asset Inventory (PAI) to account for 100% of all personnel assigned and attached to 34TH
V l x w x h Reg ( .21 15x10.02x h .21 150.3 h H .0014 cm
2. Refer to the above table to answer this question. Suppose that Mia has a budget of $7 and the price of a litre of soya milk is $1, what is the maximum quantity that Mia might purchase?
27. A budget is a specific plan of how a person or family will spend their money.
d. Logistical Supportability: (1) Deployability: required resources (less is better), (2) Infrastructure Needs: in-country evaluation of runways, road, bridges and other permanent structures which are required for combat operations (more is better), (3) Supportability: evaluation of required classes of supply and combat support personnel (less is better)
A) 6.0 m, 26.0 m B) 26.0 m, 4.0 m C) 26.0 m, 26.0 m D) 4.0 m, 4.0 m
15) In an unbalanced transportation problem where total supply exceeds total demand, the supply constraints will typically have "≥" inequalities.
Ho Yuk Him (Date of experimentation :20th and 29th October, 2010) This paper presents a study on the application of dimensional analysis on the formulation of an equation concerning the periodic time of a rod rotating at an angle about the vertical axis suspended by two strings at each end. We find that period is inversely related to distance between the strings parallel to each other and directly proportional to the both the square root of length of string and the length of suspension, (i.e.
Philip Chin has a total marketing budget of $308,000, but after salaries, fees, and planned marketing programs, only $54,000 remains for the discretionary marketing program. Evaluate each of the following four marketing programs for criteria listed (one sentence for each criteria):
2. The time taken for the pendulum to complete 20 oscillations was found and recorded.