3434 Middy

T/F: When the objective function can increase without ever contacting a constraint in the LP (linear programming) problem, we call such solution "infeasible".

False

T/F: When using ANOVA, we decompose variance into within-group and between-group variances, then calculate F statistics as within-group (MSE) over between-group variance (MSG).

False

T/F: While descriptive analytics and prescriptive analytics are related, descriptive analytics and predictive analytics are not.

False, they are all related.

Krouscas Foods makes a special blend of oil that is popular in Greek cooking. They import oil from two vendors and blend it to ensure that the resulting product contains at least 40% olive oil, 20% sunflower oil, and at least 30% corn oil. Vendor 1 can provide an oil containing 50% olive oil, 10% sunflower oil, and 40% corn oil at a cost of $9 per gallon. Vendor 2 can provide an oil containing 20% olive oil, 60% sunflower oil, and 20% corn oil at a cost of $8 per gallon. If Krouscas wants to produce 30 gallons of its special blend of Greek cooking oil at minimum cost, how much oil should it buy from each vendor?

MC: Which of the following LP problem set up is incorrect? 𝑋_1 = 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 𝑡𝑜 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑓𝑟𝑜𝑚 𝑣𝑒𝑛𝑑𝑜𝑟 1 𝑋_2 = 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 𝑡𝑜 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑓𝑟𝑜𝑚 𝑣𝑒𝑛𝑑𝑜𝑟 2 MIN: 9 𝑋1 + 8 𝑋2 ... (1) S.T. . 5 𝑋1 + .2 𝑋2 > .4(𝑋1 + 𝑋2) ... (2) . 2 𝑋1 + .6 𝑋2 > .2(𝑋1 + 𝑋2 ) ... (3) 4 𝑋1 + .2 𝑋2 > .3(𝑋1 + 𝑋2 ) ... (4) 𝑋1 + 𝑋2 = 30𝑋1 𝑋1,𝑋2 ≥ 0 - (1) - (2) - (3) ------> correct - (4)

MC: What does the Excel "=SUMPRODUCT(A1:A5,C6:C10)" function do? - Sums each range and multiplies the sums. - Sum each pair of cells and multiples each sum. - Multiplies the contents of cells containing the =SUM() command. - Multiplies each pair of cells in two arrays matched by position and sum the products.

Multiplies each pair of cells in two arrays matched by position and sum the products.

MC: Which of the following matches between the category of the analytical model and the technique is incorrect? - Predictive - Regression - Descriptive - Statistics - Predictive - Simulation - Prescriptive - Linear Programming

Predictive - Simulation

MC: The following linear programming problem has been written to plan the production of three products. 𝑋1, 𝑋2 = the number of products 1, 2 produced in each batch MAX: 20𝑋1 + 30𝑋2 S.T. 3𝑋1 + 3𝑋2 ≤ 300 --> resource 1 5𝑋1 + 4𝑋2 ≤ 600 --> resource 2 4𝑋1 + 2𝑋2 ≤ 140 --> resource 3 As a data analyst, you write the objective function and the constraints. Which of the following statement is incorrect? - The constraint regarding resource 3 is redundant - The profit that comes from selling each product is $20, and $30. - The maximum production size of 𝑋2 is 70. - We should also include nonnegativity condition, as we cannot produce negative number of products.

The constraint regarding resource 3 is redundant

T/F: Rounding the LP relaxation solution up or down to the nearest integer may produce an infeasible solution.

True

T/F: The three common elements of an optimization problem are decisions, constraints, and objective.

True

MC: What is incorrect about hypothesis testing? - We convert the test statistics to p-value before deciding whether to reject the null. - We fail to reject the null when the p-value is smaller than the significance level (𝛼). - We reject the null when the absolute value of test statistics from the sample is greater than the absolute value of critical value. - Smaller p-value indicates that we are more inclined to reject the null.

We fail to reject the null when the p-value is smaller than the significance level (𝛼).

MC: Which of the following is the general format of an objective function? - 𝑓(𝑋1, 𝑋2, ... , 𝑋𝑛) - 𝑓(𝑋1, 𝑋2, ... , 𝑋𝑛) ≥ b - 𝑓(𝑋1, 𝑋2, ... , 𝑋𝑛) ≤ b - 𝑓(𝑋1, 𝑋2, ... , 𝑋𝑛 ) = b

𝑓(𝑋1, 𝑋2, ... , 𝑋𝑛)

MC: Which of the following point is not a corner point after solving the following LP problem graphically? MAX: 4 𝑋1 + 3 𝑋2 S.T. 6 𝑋1 + 7 𝑋2 ≤ 84 𝑋1 ≤ 10 𝑋2 ≤ 8 𝑋1, 𝑋2 ≥ 0 (Graph on paper) - (0, 8) - (4.67, 8) - (10, 0) - (10, 2.33)

(10, 2.33)

MC: When do alternate optimal solutions occur in LP models? - When a binding constraint is parallel to a level curve - When a constraint is parallel to another constraint - When a non-binding constraint is perpendicular to a level curve. - Alternate optimal solutions indicate an infeasible condition.

- When a binding constraint is parallel to a level curve

MC: The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. 𝑋1 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 1 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑖𝑛 𝑒𝑎𝑐ℎ 𝑏𝑎𝑡𝑐ℎ 𝑋2 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 2 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑖𝑛 𝑒𝑎𝑐ℎ 𝑏𝑎𝑡𝑐ℎ 𝑀𝐴𝑋: 150𝑋1 + 250𝑋2 𝑆. 𝑇. 2𝑋1 + 5𝑋2 ≤ 200 − 𝑟𝑒𝑠𝑜𝑢𝑟𝑐𝑒1 3𝑋1 + 7𝑋2 ≤ 175 − 𝑟𝑒𝑠𝑜𝑢𝑟𝑐𝑒2 𝑋1,𝑋2 ≥ 0 How many units of resource 2 are consumed by each unit of product 1 produced? - 2 - 3 - 5 - 7

3