Problem 3. (9 marks in total) An iron foundry has a firm order to produce 1000...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Problem 3. (9 marks in total) An iron foundry has a firm order to produce 1000 pounds of castings containing at least 0.45 percent manganese and between 3.25 percent and 5.50 percent silicon. As these particular castings are a special order, there are no suitable castings on hand. The castings sell for $0.45 per pound. The foundry has three types of pig iron available in essentially unlimited amounts, with the following properties: Type of pig iron A Silicon 4% Manganese 0.45% B Pig A Pig B Pig C Manganese 1% 0.5% C 0.6% 0.4% Further, the production process is such that pure manganese can also be added directly to the melt. The costs of the various possible inputs are: $21/thousand pounds $25/thousand pounds $15/thousand pounds $ 8/pound. It costs 0.5 cents to melt down a pound of pig iron. A possible formulation of this problem is given as follows: Decision variables: x₁ = Pounds of pig iron A, x₂ = Pounds of pig iron B, x3 = Pounds of pig iron C, x4 Pounds of pure manganese max 0.424x, +0.42x₂ +0.43x₂ -7.55x4 s.t. x₁ + x₂ + x₂ + x₁ = 1000 (Order) (Minimum silicon concentration) 0.04x, +0.01x₂ +0.006x, 232.5 0.04x, +0.01x₂ +0.006x, ≤55 (Maximum silicon concentration) 0.0045x, +0.005x₂ +0.004x3+x24.5 (Minimum manganese concentration) X₁, X₂, X3, X₂ 20 The problem has been solved with a software, which outputted the following results: OBJECTIVE FUNCTION VALUE 1) VARIABLE X1 X2 X3 X4 424.4398 VALUE 779.431274 0.000000 220.457962 0.110727 ROW SLACK OR SURPLUS 1) 2) 3) NO. ITERATIONS- 0.000000 0.000000 22.500000 0.000000 0 REDUCED COST 0.000000 0.001753 0.000000 0.000000 DUAL PRICES 0.462401 -0.058641 0.000000 -8.012402 (a) (1 mark) What is the optimal value of the problem? (b) (2 marks) What is the optimal solution obtained by the software? (c) (2 marks) Interpret the reduced cost associated with the variable x2. (d) (2 marks) What are the binding constraints? Please, justify your answers. (e) (2 marks) What would be the effect on the objective value (optimal profit) if one additional pound of castings were ordered? Please, explain your answers. Problem 3. (9 marks in total) An iron foundry has a firm order to produce 1000 pounds of castings containing at least 0.45 percent manganese and between 3.25 percent and 5.50 percent silicon. As these particular castings are a special order, there are no suitable castings on hand. The castings sell for $0.45 per pound. The foundry has three types of pig iron available in essentially unlimited amounts, with the following properties: Type of pig iron A Silicon 4% Manganese 0.45% B Pig A Pig B Pig C Manganese 1% 0.5% C 0.6% 0.4% Further, the production process is such that pure manganese can also be added directly to the melt. The costs of the various possible inputs are: $21/thousand pounds $25/thousand pounds $15/thousand pounds $ 8/pound. It costs 0.5 cents to melt down a pound of pig iron. A possible formulation of this problem is given as follows: Decision variables: x₁ = Pounds of pig iron A, x₂ = Pounds of pig iron B, x3 = Pounds of pig iron C, x4 Pounds of pure manganese max 0.424x, +0.42x₂ +0.43x₂ -7.55x4 s.t. x₁ + x₂ + x₂ + x₁ = 1000 (Order) (Minimum silicon concentration) 0.04x, +0.01x₂ +0.006x, 232.5 0.04x, +0.01x₂ +0.006x, ≤55 (Maximum silicon concentration) 0.0045x, +0.005x₂ +0.004x3+x24.5 (Minimum manganese concentration) X₁, X₂, X3, X₂ 20 The problem has been solved with a software, which outputted the following results: OBJECTIVE FUNCTION VALUE 1) VARIABLE X1 X2 X3 X4 424.4398 VALUE 779.431274 0.000000 220.457962 0.110727 ROW SLACK OR SURPLUS 1) 2) 3) NO. ITERATIONS- 0.000000 0.000000 22.500000 0.000000 0 REDUCED COST 0.000000 0.001753 0.000000 0.000000 DUAL PRICES 0.462401 -0.058641 0.000000 -8.012402 (a) (1 mark) What is the optimal value of the problem? (b) (2 marks) What is the optimal solution obtained by the software? (c) (2 marks) Interpret the reduced cost associated with the variable x2. (d) (2 marks) What are the binding constraints? Please, justify your answers. (e) (2 marks) What would be the effect on the objective value (optimal profit) if one additional pound of castings were ordered? Please, explain your answers.
Expert Answer:
Answer rating: 100% (QA)
a Optimal value 4244398 the first line of the solution re... View the full answer
Related Book For
Data Analysis and Decision Making
ISBN: 978-0538476126
4th edition
Authors: Christian Albright, Wayne Winston, Christopher Zappe
Posted Date:
Students also viewed these accounting questions
-
A foundry uses 3,600 tons of pig iron per year at a constant rate. The cost per ton delivered to the foundry is $145. It costs $92 to place an order and $18 per ton per year for storage. Find the...
-
Iron containing 0.05% C is heated to 912 C in an atmosphere that produces 1.20% C at the surface and is held for 24 h. Calculate the carbon content at 0.05 cm beneath the surface if (a) The iron is...
-
The Iron Pit Foundry manufactures dumbbells for gyms. The Iron Pit's owners, Matt Andrews and Doug Ballard, provide you with the following information regarding raw materials (cast iron & steel): Raw...
-
Consider the following actual FY2019 data and a forecast of FY2020 selected balance sheet and income statement numbers. $ millions FY2019 Actual FY2020 Est. $29,009 $32,102 14,592 16,051 8,755 9,923...
-
Tylers Consulting Company has purchased a new $15,000 copier. This overhead cost will be shared by the purchasing, accounting, and information technology departments since those are the only...
-
You are designing a two-string instrument with metal strings 35.0 cm long, as shown in Fig. P15.58. Both strings are under the same tension. String S 1 has a mass of 8.00 g and produces the note...
-
Background inventory data represent average environmental interventions related to a particular material used in a particular industry.Who supplies such information? Why has background inventory data...
-
On January 1, 2016, Parflex Corporation exchanged $344,000 cash for 90 percent of Eagle Corporation's outstanding voting stock. Eagle's acquisition date balance sheet follows: On January 1, 2016,...
-
Thomas Company's Year 1 asset turnover was 2.0. The firm's total assets were $10,000,000 at January 1, Year 1 and $12,400,000 at December 31, Year 1. Net sales fo Year 1 were:
-
Block C starts from rest and moves down with a constant acceleration. Knowing that after block A has moved 0.5 m its velocity is 0.2 m/s, determine(a) The accelerations of A and C,(b) The velocity...
-
Jayne is a Canadian who owns a hotel in Savannah, Georgia. When she brings her investment income back to Canada, how is this income classified? Explain.
-
1. how did the differences between rules-based and principle-based standards influence the debate and ultimately the final revenue recognition accounting standard issued by both standard-setters? 2....
-
Moderator in a nuclear reactor. When fast neutrons are produced in a nuclear reactor, they must be slowed before they can participate in a chain-reaction process. This is done by allowing them to...
-
A 4.00 kg mass is sitting at rest on a horizontal surface. A horizontal force of 9.30 Newtons is needed to start this mass sliding across the surface. What is the coefficient of static friction...
-
A 39.0 V motional emf was generated in the Earth's 4.7010-5 T field, while moving at 7.90103 m/s. What was the angle between the shuttle's velocity and the Earth's field, assuming the conductor was...
-
On June 1, 2022, Gamma Corporation paid $240,000 cash for one year's rent in advance and recorded the transaction with a debit to Prepaid Rent. The December 31, 2020 adjusting journal entry is: Debit...
-
Securities within an asset class are often Asset classes themselves are often Uncorrelated, uncorrelated, negatively correlated Highly correlated, uncorrelated, negatively correlated Highly...
-
In Exercises find dy/dx by implicit differentiation. xy - y = x
-
Recall that the file Supermarket Transactions.xlsx contains over 14,000 transactions made by supermarket customers over a period of approximately two years. Use Excel filters to answer the following...
-
SoftBus believes it can afford to spend much less time with customers who own PCs and score at least 4 on PCKnowledge. Lets call these the PC-savvy customers. On the other hand, SoftBus believes it...
-
The file S02_21.xlsx contains monthly interest rates on 30-year fixed-rate mortgages in the United States from 1977 to 2009. The file also contains rates on15-year fixed-rate mortgages from late 1991...
-
Air passes through a normal shock in a supersonic wind tunnel. Upstream conditions are \(M_{1}=1.8, T_{1}=270 \mathrm{~K}\), and \(p_{1}=\) \(10.0 \mathrm{kPa}\) absolute. Downstream conditions are...
-
A Boeing 747 cruises at \(M=0.87\) at an altitude of \(13 \mathrm{~km}\) on a standard day. A window in the cockpit is located where the external flow Mach number is 0.2 relative to the plane...
-
Air flows isentropically through a converging nozzle into a receiver where the pressure is \(250 \mathrm{kPa}\) absolute. If the pressure is \(350 \mathrm{kPa}\) absolute and the speed is \(150...
Study smarter with the SolutionInn App