LINEAR PROGRAMMING

A firm produces ties using various materials. Their aim, as most firms in the economy, is to maximize profit but they face some production constraints. Your task is to find the optimal solution by applying linear programming using Excel. Your results need to show the values for each decision variable, and the maximum profit subject to the constraints. The Excel sheet need to be uploaded on the student portal, and a print screens of the pages need to be copied on Word document (stating your name and student ID), and handed over in class on May 5th 2017. DUBAI Ties is a firm, based in Deira, that produces four varieties of ties:  Two are blends of polyester and cotton  One is expensive all-silk  One is all-polyester The table on the below shows the cost and availability of the three materials used in the production process: MATERIAL COST PER YARD ($) MATERIAL AVAILABLE PER MONTH (YARDS) Silk 24 1,200 Polyester 6 3,000 Cotton 9 1,600 The firm has contracts with several major department store chains to supply ties.  Contracts require a minimum number of ties but may be increased if demand increases.  Their goal is to maximize monthly profit given the decision variables stated below. Decision variables: X1 = number of all-silk ties produced per month X2 = number all-polyester ties X3 = number of blend 1 polyester-cotton ties X4 = number of blend 2 silk-cotton ties 3 | P a g e DATA PROVIDED: VARIETY OF TIE SELLING PRICE PER TIE ($) MONTHLY CONTRACT MINIMUM MONTHLY DEMAND MATERIAL REQUIRED PER TIE (YARDS) MATERIAL REQUIREMENTS All silk 19.24 5,000 7,000 0.125 100% silk All polyester 8.70 10,000 14,000 0.08 100% polyester Poly – cotton blend 1 9.52 13,000 16,000 0.10 50% polyester – 50% cotton Silk-cotton blend 2 10.64 5,000 8,500 0.11 60% silk - 40% cotton 4 | P a g e PROBLEM 2: LINEAR PROGRAMMING USING GRAPHICAL REPRESENTATION An ice cream company is involved in the production of two different tastes: Cherry and Kiwi. Two resources needed to produce Cherry and Kiwi ice cream are Milk and Sugar. The table below gives the required amount for each item: ITEM UNITS/MILK KG/SUGAR Cherry ice cream 4 5 Kiwi ice cream 6 2 The company has 200 units of Milk available and 150 Kg Sugar available. The revenue received for each item produced (all production is sold) is AED 400 for a pack of Cherry Ice cream (2Kg) and AED 600 for a pack of Kiwi Ice cream (2Kg). i. Determine the Decision variables ii. Formulate the Profit Objective Function iii. Formulate the production constraints iv. Determine the feasible region (graphically) v. Draw at least three Iso-profit lines vi. Determine the optimal solution. 5 | P a g e PROBLEM 3: Decision tree analysis The Dubai Multi-Group (DMG) is set up to conduct soil explorations in order to ascertain whether significant metal deposits that are worthy of further commercial exploitation are present or not. Current DMG has an option to purchase outright a parcel of land for £3m. If it purchases this parcel of land then it will conduct a geological exploration of the land. Past experience indicates that for the type of parcel of land under consideration geological explorations cost approximately £1m and yield significant metal deposits as follows: GOLD 0.05% chance SILVER 0.2% chance PLATINUM 1% chance Only one of these three metals is ever found (if at all), i.e. there is no chance of finding two or more of these metals and no chance of finding any other metal. If Platinum is found then the parcel of land can be sold for £30m, if gold is found then the parcel of land can be sold for £250m and if silver is found the parcel of land can be sold for £150m. DMG can, if they wish, pay £750,000 for the right to conduct a three-day test exploration before deciding whether to purchase the parcel of land or not. Such three-day test explorations can only give a preliminary indication of whether significant metal deposits are present or not and past experience indicates that three-day test explorations cost £250,000 and indicate that significant metal deposits are present 50% of the time. If the three-day test exploration indicates significant metal deposits then the chances of finding Platinum, Gold and Silver increase to 3%, 2% and 1% respectively. If the three-day test exploration fails to indicate significant metal deposits then the chances of finding Platinum, Gold and Silver decrease to 0.75%, 0.04% and 0.175% respectively. QUESTIONS: 1. Draw the decision tree, showing all values. 2. What would you recommend MDG should do and why? 3. Interestingly, information exists that a Sharjah company working in a related field to DMG is prepared to pay half of all costs associated with this parcel of land in return for half of all revenues. Under these circumstances what would you recommend DMG should do and why?