ADM 3301 Sample Mid-term Exam Duration: 2.5 hours Student name:_______________________ Student No.__________________ INSTRUCTIONS: 1- Write down the exam copy number (that exists at the top right corner of this page) on the identification white card next to your name. 2- Verify that your exam has 9 pages (including this title page). 3- Answer all questions on your examination copy. Use the opposite (blank) side‚ if necessary. Answers or calculations written on the sheet
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such that the following two conditions on the random vector [pic]are met: 1. [pic] 2. [pic] the best (minimum variance) linear (linear functions of the [pic]) unbiased estimator of [pic]is given by least squares estimator; that is‚ [pic]is the best linear unbiased estimator (BLUE) of [pic]. Proof: Let [pic]be any [pic]constant matrix and let [pic]; [pic] is a general linear function of [pic]‚ which we shall take as an estimator of [pic]. We must specify the elements of [pic]so that [pic]will be
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Operations Research Modeling Toolset Network Problems Linear programming has a wide variety of applications Network problems Special types of linear programs Particular structure involving networks Ultimately‚ a network problem can be represented as a linear programming model However the resulting A matrix is very sparse‚ and involves only zeroes and ones This structure of the A matrix led to the development of specialized algorithms to solve network problems Types of Network Problems
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18 16 25 29 24 When the metals are processed and refined‚ the impurities are removed. The company wants to know the amount of each ore to use per ton of the alloy that will minimize the cost per ton of the alloy. a. Formulate a linear programming model for this problem. b. Solve the model by using the computer. 19. As a result of a recently passed bill‚ a congressman’s district has been allocated $4 million for programs and projects. It is up to the congressman
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find only one straight line. If r=0‚ i.e. both the variance are independent then the two lines will cut each other at a right angle. In this case the two lines will be ║to x and y axis. The Graph is given below:- We restrict our discussion to linear relationships only that is the equations to be considered are 1- y=a+bx 2- x=a+by In equation first x is called the independent variable and y the dependent variable. Conditional on the x
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conditions I believe that the results shown in the distance vs. time graph will have a curve showing increasing speed or in other words‚ increasing velocity over time. Therefore‚ the results shown in the velocity vs. time graph will have a positive linear slope. The acceleration vs. time graph will then have no slope and just a straight line because the change of velocity is relatively constant. In conclusion‚ when the mass of the weight increases‚ the acceleration won’t and only the speed and velocity
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causing shortening in the direction of force) Strain • If a bar is subjected to a direct load‚ and hence a stress‚ the bar will changes in length. If the bar has an original length L and change in length by an amount δL‚ the linear strain produced is defined as‚ Linear strain‚ ε=Original length (L) / Change in length (δL ) • Strain is a dimensionless quantity. Stress- Strain curve for mild steel • Elastic limit : It is the stress beyond which the material will not return to its original
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platinum‚ whereas each bracelet requires 2 ounces of gold and 5 ounces of platinum. The store has to use a minimum of two ounces of gold. The demand for bracelet is no less than three. A necklace earns $375 in profit and a bracelet‚ $225. Formulate a linear programming model for this problem with an appropriate objective function =number of necklaces to be made = number of bracelets to be made Maximize Profit (Z)= Subject to Maximum availability of gold Minimum usage quantity of gold Maximum availability
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column B. The weekly sales (y units) in each market area was then recorded as shown in column C. 1. Use linear regression to estimate a linear equation describing how the value of sales (y) varies with the level of the fitted equation. 2. Assess the validity of the fitted equation. 3. If the product sells at a price of $100 and costs $70 per unit to produce‚ estimate a linear equation for the company’s weekly profit in terms of its advertising expenditure (x). DATA SET 3 The
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The following table gives the time‚ in minutes‚ to perform the tasks at each assembly point for the individual teams. Assembly 2 26 24 26 24 26 Point 3 40 30 28 36 30 4 30 32 36 30 40 5 26 18 18 20 24 Team A B C D E 1 20 22 24 20 20 Formulate a linear programming model that will minimize the total assembly time for a printer. 6. Why is implementation a difficult aspect of the quantitative modeling process? Caston Sigauke 2006 1 7. A post office requires different numbers of full-time employees
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