Tjs inc makes three nut mixes

MSCI 2200 UT Quantitative Decision Models Problem Solving LP Questions
Subject
Business Finance

Course
MSCI 2200

School
University of Toronto

Department
MSCI

Question Description
For each question, state your model by clearly defining your decision variables (with appropriate units), the objective function, and all the relevant (including the non-negativity) constraints. The graphical solution to Question #5 could be hand-drawn, but you must submit a jpg or pdf file of your graph

MSCI-2200 Quantitative Decision Models I Assignment #1 2020 Fall Term Due Date: Thursday, October 22, 2020 Instructions: 1. Assignments are only accepted electronically through Blackboard. The server is open to accept your submission until 11:55 p.m. on October 22, 2020. Please allow sufficient time for the server to complete your submission and last-minute technical failures are not acceptable reasons for extensions. No late assignments will be accepted. 2. For each question, your mathematical model and answers to each individual part should be typed in Microsoft Word. For each question, state your model by clearly defining your decision variables (with appropriate units), the objective function, and all the relevant (including the non-negativity) constraints. The graphical solution to Question #5 could be hand-drawn, but you must submit a jpg or pdf file of your graph. 3. Except for Question #5, where graphical solution is required, you only need to give the model formulation, no solution required. Question #1: Web Mercantile sells many household products through an on-line catalog. The company needs substantial warehouse space for storing its goods. Plans now are being made for leasing warehouse storage space over the next five months. Just how much space will be required in each of these months is known. However, since these space requirements are quite different, it may be most economical to lease only the amount needed each month on a monthby-month basis. On the other hand, the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for the entire five months. Another option is the intermediate approach of changing the total amount of space leased (by adding a new lease and/or having an old lease expire) at least once but not every month. The space requirements for the next five months are given below: Month Required Space 1 2 3 4 5 30,000 sq. ft. 20,000 sq. ft. 40,000 sq. ft. 10,000 sq. ft. 50,000 sq. ft. and the leasing costs for the various leasing periods are as follows: 1 Leasing Period (# of months) Cost per Sq. Ft. Leased 1 2 3 4 5 $65 $100 $135 $160 $190 The objective is to minimize the total leasing cost for meeting the space requirements. a) Identify verbally the decisions to be made, the constraints on these decisions, and the overall measure of performance for the decisions. b) Summarize the model in algebraic form by stating the decision variables, the objective function and constraints. Hint: Define your decision variables as Xij = amount of space leased in month i for a period of j months for i = 1, …, 5 and j = 1, …, 6 – i; for example, X24 = amount of space leased in month 2 for a period of 4 months. This problem has 15 variables. Question #2: Larry Edison is the Director of the Computer Center for Buckly College. He now needs to schedule the staffing of the center. It is open from 8 AM until midnight. Larry has monitored the usage of the center at various times of the day and determined that the following numbers of computer consultants are required: Minimum Number of Consultants Required Time of Day to be on Duty 8 AM -noon 4 Noon – 4 PM 8 4 PM – 8 PM 10 8 PM - Midnight 6 Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for eight consecutive hours in either one of the following two shifts: morning (8 AM – 4 PM), and evening (4 PM – Midnight). Full-time consultants are paid $14.00 per hour. Part-time consultants can be hired to work any of the four shifts listed in the table. Parttime consultants are paid $12.00 per hour. An additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty. 2 Larry would like to determine how many full-time and part-time consultants should work each shift to meet the above requirements at the minimum possible cost. Summarize the model in algebraic form by defining the decision variables, the objective function and all the constraints. Question #3: TJ’s, Inc., makes three nut mixes for sale to grocery chains located in the Southeast. The three mixes, referred to as the Regular Mix, the Deluxe Mix, and the Holiday Mix, are made by mixing different percentages of five types of nuts. In preparation for the fall season, TJ’s has just purchased the following shipments of nuts: Type of Nut Almond Brazil Filbert Pecan Walnut Shipment Amount (pounds) 6000 7500 7500 6000 7500 The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25% filberts, 10% pecans, and 25% walnuts. The Deluxe Mix consists of 20% of each type of nut, and the Holiday Mix consists of 25% almonds, 15% Brazil nuts, 15% filberts, 25% pecans, and 20% walnuts. TJ’s accountant analyzed the cost of packaging materials, sales price per pound, and so forth, and determined that the profit contribution per pound is $1.65 for the Regular Mix, $2.00 for the Deluxe Mix, and $2.25 for the Holiday Mix. Customer orders already received are summarized here: Type of Mix Regular Deluxe Holiday Order (pounds) 10,000 3,000 5,000 Because demand is running high,