All the assumptions of linear programming hold. a. Formulate and solve a linear programming model for this problem on a spreadsheet. b. Formulate this same model algebraically.
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- May I have the linear programming graph (or model) or plot with the given following information? 3 variables and 8 contraints Objective - Zmax = 1.85R+2.1D+2.15H Constraints: 0.15R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.15H ≤ 7500 0.25R + 0.2D + 0.15H ≤ 7500 0.10R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.20H ≤ 7500 R ≥ 10000 D ≥ 3000 H ≥ 5000Exercise 4 a) Write the objective function of this LP.b) Write the constraint of the basic element Y.c) Write the constraint that expresses"the factional contributions from each mine must add up to 1."d) What is the optimal fraction of a ton to be chosen from mine 4?e) To make the optimal fraction of a ton to be chosen from mine 4 non-zero, how should the cost per ton of ore from mine 4 change?f) If the minimum requirement amounts of basic element X increases to 7 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?g) If the minimum requirement amount of basic element Z decreases to 25 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?5. Christy Crafty Boat Supplies has 250 yards of canvas to make sails and deck covers. There are205 hours of labor available. The following data apply:Profit Canvas LaborSail $50 35 yards 10 hoursDeck Cover 65 10 15How many of each should be made to maximize profit? 6. KitchenKorp produces three electrical appliances: blenders and can openers. These products havethe following resource requirements.ProductResource RequirementsCost/Unit Labor hours/UnitCan OpenerBlender$172056There is a maximum of 1,000 hours of labor available during the coming period. Maximum customerdemand during this time is 150 for each of the products. Selling prices are $35 for a can opener and$45 for a blender. How many of each should be made to maximize profits?
- #1- Maxwell Manufacturing makes two models of felt tip marking pens. Requirements and available resources for each lot of pens are given in the following table: Fliptop Model Tiptop Model Available Plastic 3 4 36 Ink Assembly 5 4 40 Molding Time 5 2 30 The profit for either model is $1,000 per lot. a) What is the linear programming model for this problem? b) Using Microsoft Excel's Solver, find the optimal solution. How many Fliptop models and how many Tiptop models should be produced? What is the maximum profit? c) Will there be excess capacity in any resource? Use Excel's Solver and run a sensitivity report to answer the following questions. d) Over which range can the objective function coefficient for Fliptop Models change without affecting the original optimal solution? What is this range called? e) What is the shadow price (dual price) for the plastic constraint and how would you interpret it? f) What is the shadow price (dual price)…A young engineer is considering establishing his own small company.An investment of Php 100,000 will be required which must be recovered in 15years . It is estimated that sales will be Php 150,000 per year and thatoperating expenses will be as follows:Material Php 40,000 per yearLabor Php 70,000 per yearOverhead Php 10,000 + 10% of sales/yearSelling expenses Php 5,000/yearThe young engineer will give up his regular job paying Php 150,000 per yearand devote full time to the operation of the business. This will result indecreasing labor by Php 10,000 per year , material cost by Php 7000 peryear, and overhead cost by Php 8000 per year. If the young engineer expectsto earn at least 20% on his capital, should he invest ?graph the following constraints: x + y <= 60 15x + 30y <= 20 0.9y > = 0.10x x > = (2/3) y Explan in detail
- A. Write a document with the following information: 1. What do you expect your job to pay when you start? 2. What benefits are musts for you? 3. What benefits would you like to have even though they are not musts? 4. Include the graph you generate in step B below. B. Create a spreadsheet and a graph of life vs funds For each year of your remaining life specify the amount you plan to save/invest/withdraw that year and how much you expect that amount to increase during the year (base on actual data – typical savings interest rate, typical stock market interest rate, typical CDs, typical…). Calculate how much your funds will increase/decrease over your life and create a life (x-axis) vs funds (y-axis) plot.Hot Oven daily requirements of 70 g of protein, 1 g calcium, 12 mg iron, and 3000 calories are needed for a balanced diet. The following foods are available for consumption with the cost and nutrients per 100 g as shown. protien (g) calories calcium(g) iron(mg) cost (ghc) brown bread 12.0 246 0.1 3.2 0.5 cheese 24.9 432 0.2 0.3 20 butter 0.1 793 0.03 0.0 1.0 baked beans 6.0 93 0.05 2.3 0.25 spinach 3.0 26 0.1 2.0 0.25 The objective of the Hot Oven is to find a balanced diet with minimum cost.a) Formulate a linear programming model for this problem. b) Use solver to find optimal solution and sensitivity report. c) Management have asked you to determine the optimal solution. Write your answer in a form of a report to be submitted to the management. d) Advice the management about objective function value corresponding to your answer in (b)A manufacturing company has the following financial information (in millions of $)Sales $562Cost of goods soldDirect labor 43Purchased materials 267Overhead 35All other costs 142Pretax earnings 75a. What is the profit leverage effect of purchasing in this company?b. What is the percent increase in earnings from a 5 percent savings in purchasing?
- A manager wants to know how many units of each product to produce on a daily basis in order toachieve the highest contribution to profit. Production requirements for the products are shown inthe following table.ProductMaterial 1(pounds)Material 2(pounds)Labor(hours)A 2 3 3.2B 1 5 1.5C 6 — 2.0Material 1 costs $5 a pound, material 2 costs $4 a pound, and labor costs $10 an hour. Product Asells for $80 a unit, product B sells for $90 a unit, and product C sells for $70 a unit. Availableresources each day are 200 pounds of material 1; 300 pounds of material 2; and 150 hours of labor.The manager must satisfy certain output requirements: The output of product A should not bemore than one-third of the total number of units produced; the ratio of units of product A to units ofproduct B should be 3 to 2; and there is a standing order for 5 units of product A each day. Formulate a linear programming model for this problem, and then solveConsider the linear program below and answer the follow questions Max 3A+2B s.t. A+B >=4 3A+4B <= 24 A>=2 A-B<=0 A,B >=0 A. Graph it B. Write in standard form C. Solve the problem D. What are the values of the slack and surplus variables at the optimal solution?ABC Cabinets received a contract to produce bookshelf speakers (BS) and floor speakers (FS) over the next 2months. The contract says ABC must deliver 2100 BS and 1500 FS at the end of month 1 and deliver 1200 BS and2600 FS at end of month 2. The time to make a BS is 0.7hr and a FS is 1hr. Raw material costs $10 for each BSand $12 for each FS and there is an unlimited amount available. Labor costs are $22/hr using regular productiontime and $33/hr using overtime. ABS has up to 2400hrs of regular production time each month and up to 1000additional hours of overtime each month. Any cabinets left at the end of month 1 can be stored for $5/cabinet.(a) Formulate an LP to determine the number of units that should be manufactured each month on regular andovertime to minimize total production and storage costs
