Read the case study below and answer the following questions. A foundry that specialises in custom blended alloys has received an order for 1000kg of an alloy containing at least 5% chromium and not more than 50% iron. Four types of scrap that can be easily acquired can be blended to produce the order. The cost and metal characteristics of the four scrap types are given below: a) Define your decision variables explicitly. (10) b) Formulate this optimisation problem as a linear program. (20) c) Solve this model using Solver. (20) d) Write down the optimal solution and the associated total costs. (5) Use only the initial printout of the optimal solution to answer the following questions. (This means that you may not change the relevant parameters in the model and do re-runs.) Explain how you arrive at your answers. a) How good a deal would the purchasing manager need to get on scrap type 1 before he would be willing to buy it for this order? (5) b) Upon further investigation, the purchasing manager finds that scrap type 2 is now being sold at R5,40 per kg. Will the purchasing plan change? By how much will the cost of purchasing the metals increase? (8) c) The customer is willing to raise the ceiling on the iron content to negotiate a reduction in price he pays. How should the purchasing manager react to this? (7) d) The customer now specifies that the alloy must contain at least 6% chromium. Can the purchasing manager comply with this new specification? Will the price charged for the order change? Your answers to the above will be assessed in terms of the level of communication displayed, the insights and inferences drawn, and your ability to show the implications of the factors that you have assessed and discussed. An answer that merely gives a list of events that have happened or a synopsis of a situation, without showing insight into the reasons and results, will not earn good marks. Your method of referencing must consistently follow the Augmented Harvard method. Annexures can be used to attach additional information. Marking guideline/matrix/rubric The following template will be used in the overall assessment of your assignments: approprlate aniu mediniglul. The analysis is appropriate, meaningful and beyond the Obvious. 40 to 59 Acceptable Some indication of understanding (average to Somewhat integrated and linked to relevant concepts good) Description of company is appropriate, with substantial Content. Analysis is appropriate with substantial content. 0 to 39 Very poor, Content has been regurgitated. poor to fair Not consistently linked and integrated; somewhat disjointed Description of company's current state is inappropriate and Superficial. Analysis inappropriate and superficial Structure Score Level Criteria 7,5 to 10 Very good to Logical and well structured excellent All elements of the report are present and well linked. Good flow from section to section 5 to 7 Average to Somewhat logical structure good Most of the elements present in the report Evidence of an attempt to link the elements 0 or 4,5 Very poor to fair Lacking structure Illogical Most of the elements of the report absent Language use and grammar 10% of total marks Score Level Criteria 7,5 to 10 Very good to excellent 5 to 7 Average to good 4 or 4,5 Poor to fair Below 4 Very poor Consistent and very professional (fewer than four errors of punctuation, grammar and spelling) All references complete and accurate and listed in the report Minor problems in sentence construction; some errors of word choice but the meaning is clear. A few spelling, grammar and punctuation errors. Vocabulary limited; frequent errors of word choice. Meaning is confused or obscured. Many spelling, grammar and punctuation errors. Little knowledge of English vocabulary, grammar, spelling and punctuation Does not communicate