3.5-5.* Fred Jonasson manages a family-owned farm. To supple- ment several food products grown on the farm, Fred also raises pigs for market. He now wishes to determine the quantities of the available types of feed (corn, tankage, and alfalfa) that should be given to each pig. Since pigs will eat any mix of these feed types, the objective is to determine which mix will meet certain nutri- tional requirements at a minimum cost. The number of units of each type of basic nutritional ingredient contained within a kilogram of each feed type is given in the following table, along with the daily nutritional requirements and feed costs:

2. Prove or disprove: If a canonical LP problem Maximize: subject to

MATH 308 - Assignment 1 1. Find necessary and sufficient conditions for the numbers s and t to make the LP problem Maximize: f(x1, x2) = x1+x2 subject to sx1+tx2 ≤ 1 x1, x2 ≥ 0 a) have an optimal solution. b) be infeasible. c) be unbounded. Prove your answers.

A shoe store orders shoes from the manufacturer and sells them at a mall. Storing shoes at the store costs $2 per shoe pair for a year. When reordering shoes from the manufacturer, there is a fixed cost of $36 per order as well as $9 per shoe pair. The retail store sells 3500 shoe pairs each year. What is the optimal number of shoes to order in each order to minimize their total inventory costs? What is the total inventory cost?

For the previous problem, Generate an interaction plot for any interactions with large effects. Suppose the objective in Problem 2 is to minimize the What are the best settings for the factors to response.achieve this objective?

6) A Chemical manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an hour costs $4 and yields 3 units of A, 1 ofB, and 1 of C. Running process 2 for an hour costs $1 and produces I unit of A and I of B. To meet customer demands, at least 10 units of A, 5 of B, and 3 of C must be produced daily. Formulate the LP and then graphically determine a daily production plan that minimizes the cost ofmeeting company's daily demands. (20 points)

19. NIST SP 800-34 belongs to which contingency planning process element? a. Policy environment enabling the planning process b. Business impact analysis to understand causes and effects of precursor activities c. Planning methodologyС. d. Planning budget a nd access to resources e. None of the above

5. Which is the most expensive exclusive site resumption strategies? a. Mobile site b. Cold site С.Warm site d. Hot site e. Mirrored site

Find the shortest path from node 1 to 5 in the figure 3 using Dijkstra Algorithm.

Case 1:(40 Points) A national quality consultation firm has identified the following set of activities thatmust occur to carry out an audit for one of their major clients. As the project manager of thisaudit, answer the following questions related to the project plan. Q1. Draw the Network Diagram of the project plan for the consultation firm. (13 Points) Q2. Answer the following MCQ (Multiple Choice Questions), and justify your answer for the selected questions where the justification box shown (15 Points/ 3 Points Each): 1) What is the expected project completion time:а. 54 days b. 34 days c. 61 days d. 59 days 2)What is the Slack period for task C:a. 12 days b. 3 days c. 4 days d. 11 days 3)What is the task with the longest slack time:а. Task H b. Task F с. Task B d. Task J 4) What is the slack period for task G:a. 6 days b. 5 days c. 8 days d. O days 5) What is the early start for task C:a. Day 12b. Day 25c. Day 19d. Day 16 Q3. Fill in the blank the correct answer for the following statements (12 Points/ 3 Points Each): 1. The critical path the plan is showing in the project 2. The early finish for task H 3. The late start for task D 4. The late finish for task J