Computing: ISE212
Engineering MATLAB
Spring_2007
Homework #1A Due:Friday 2/16 Use the digital drop-box in blackboard to hand-in your HW to the TA. 1. Write an executable script file (m-file) that takes no input and returns a vector solving the following system of equations using matrix operations. (Determine the values of s, u, p, and w). Also, include the inverse of the left-hand coefficient 4x4 matrix. Use plenty of comments to annotate your code and include your name in the m-file. (Name your m-file>>> solve.m). 16s + 32u + 33p + 13w = 91 5s + 11u + 10p + 8w = 16 9s + 7u + 6p + 12w = 5 34s + 14u + 15p + w = 43 Ans= % Script file: solve.m % Purpose: To calculate/solve a simultaneous system of equations % Date: 02/07 Programmer: xxxxxxx % Define Variables: % A >>> 4 X 4 matrix of L-hand coefficients % B >>> 4 X 1 vector of R-hand coefficients % X >>> 1 X 4 vector of unknowns A=[16 32 33 13; 5 11 10 8; 9 7 6 12; 34 14 15 1]; B=[91; 16; 5; 43]; disp('The values of s, u, p, and w follow:') X=A\B disp('The inverse of the L-hand coefficient matrix follow:') inv(A) Running the m-file produces the following in MATLAB: The values of s, u, p, and w follow: X= -0.1258 -8.7133 11.2875 -0.0500 The inverse of the L-hand coefficient matrix follows: ans = -0.0177 -0.0023 0.0180 0.0333 -0.3344 1.2352 -0.4695 0.1000 0.3500 -1.1375 0.3875 0.0333 -0.1000 -0.1500 0.1500 -0.0333
2. Manufacturing Cost Analysis: The table below shows the hourly cost of four types of manufacturing processes. It also shows the number of hours required of each process to produce three different products. Use matrices and MATLAB to solve the following: > Determine the cost of each process to produce one unit of product 1. > Determine the cost to make one unit of each product. > Suppose you produce 10 units of product 1, 5 units of product 2, and 7 units of product 3. Provide the total cost for this scenario. Write an executable script file (m-file) that takes no inputs to return your solutions. (Name your m-file: mca.m). Table: Cost and Time Data for Manufacturing Process Hours Required to Produce One Unit Process Hourly Cost $ Product 1 Product 2 Product 3 Lathe 10 6 5 4 Grinding 12 2 3 1 Milling 14 3 2 5 Welding 9 4 0 3 Ans= % Script file: mca.m % Manufacturing Cost Analysis % Date: 2/07 Programmer: XXX hour_cost=[10 12 14 9]; hours_1=[6 2 3 4]; hours_2=[5 3 2 0]; hours_3=[4 1 5 3]; disp('Costs of each of the four processes to produce one unit of product_1:') process_cost_1=hour_cost.*hours_1 disp('Costs to produce one unit of each product:') unit_cost=hour_cost*[hours_1', hours_2', hours_3'] units=[10 5 7]; disp('The total cost to produce 10, 5, and 7 units, respectively') total_cost=units*unit_cost'