A. Graph it B. Write in standard form C. Solve the problem
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Consider 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?
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- Finance Problem 8-9 Develop a production schedule to produce the exact production requirements by varying the workforce size for the following problem. The monthly forecasts for Product X for January, February, and March are 930, 1,550, and 1,220, respectively. Safety stock policy recommends that half of the forecast for that month be defined as safety stock. There are 22 working days in January, 19 in February, and 21 in March. Beginning inventory is 550 units. Manufacturing cost is $190 per unit, storage cost is $6 per unit per month, standard pay rate is $4 per hour, overtime rate is $6 per hour, cost of stockout is $9 per unit per month, hiring and training cost is $280 per worker, layoff cost is $380 per worker, and worker productivity is 0.1 unit per hour. Assume that you start off with 47 workers and that they work 8 hours per day. (Round Workers Required up to the next higher whole number. Round all other variables off to the nearest whole number. Use…Max −A + 2B s.t. -2A + 3B ≤ 8 (Constraint 1) 6A - 2B ≤ 5 (Constraint 2) A + B ≤ 5 (Constraint 3) A ≥ 1 (Constraint 4) A, B ≥ 0 SHOW ALL CALCULATION STEPS a) Solve the LP Model using the graphical method. Label your graph completely (and upload your graph as a jpg). State your optimal solution and objective function value. b) Calculate the Slack/Surplus for each constraint. c) Calculate the Shadow/dual Prices for each constraint.the excel file president’s inn guest database provides a list of customers, rooms they occupied, arrival and departure dates, number of occupants, and daily rate for a small bed- and-breakfast inn during one month. room rates are the same for one or two guests; however, additional guests must pay an additional $20 per person per day for meals. guests staying for seven days or more receive a 10% discount. modify the spreadsheet to calculate the number of days that each party stayed at the inn and the total revenue for the length of stay.
- California MegaTech is a manufacturing company that, due to low interest rates, thinks now may be the time to finance expansion into the Los Angeles and/or San Francisco areas by building factories there. However, the company only has a $10 million capital budget. So management must decide what to build and where in order to maximize the expansion's net present value (NPV). This investment is subject to the following considerations: Net Present Value ($mil) LA SF Capital Required ($mil) LA SF Warehouse 4 Warehouse 2 Factory 8 Factory 3 The company is willing to build a factory at either or both locations. The company is willing to build no more than one factory in each location. The company is willing to build only ONE warehouse. The company is willing to build a warehouse ONLY if a factory is built at the same location. Each potential factory/warehouse has capital requirements. Each potential factory/warehouse has a positive net present value. The company is only willing to commit $10…?Q) Solve the LPP problems below by using big M-Method MIN Z=8X1+2X2 S.T X1+2X2=66 X1+6X2268 X1+4X2<82 X120,X220The distribution of daily demand for rental trucks at a vehicle rental company is shown in the following table: Relative Frequency Demand 0.07 0 0.14 1 0.15 2 0.14 3 0.12 4 0.08 5 0.3 6 Trucks are rented by the day only and the company makes $14 per rented truck per day. The rental company keeps four trucks at this location. Assuming that the stocking decision is optimal, what is the implied range of excess cost per truck per day? a. 0 and 186 b. 8.58064 and 14 c. 14 and 24.8889 d. 6 and 8.58064 e. 34.2759 and 79.3333
- 2 3 4 Chocolate 5 Nougat 6 Nuts 7 Caramel 8 9 Demand 10 Total to Make Ingredients 11 12 Price/Bar 13 Cost/Bar 14 Gross Profit/Bar 15 16 Gross Profit/Type 17 18 Total Gross Profit 19 20 21 Ingredients 22 Chocolate 23 Nougat 24 Nuts 25 Caramel 26 Milky Way 1 1 0 .1 Candy Bars Snickers 1 1 $0.90 $0.45 $0.45 1 1 Nut Roll 3 Musketeers 1 1 0 0 2,000,000 2,500,000 1,000,000 2,000,000 1,500,000 1,000,000 0 1 1 1 $0.90 $1.05 $0.65 $0.50 $0.25 $0.55 Material Totals Used Available 5,000,000 6,000,000 6,000,000 7,000,000 2,500,000 2,500,000 4,500,000 5,500,000 $900,000 $375,000 $550,000 $2,725,000 1,500,000 1,500,000 $0.90 $0.30 $0.60 $900,000 Cost $0.15 $0.15 $0.20 $0.15Problem 13-03 Algo (Solving Integer Optimization Problems with Excel Solver) Number of: Pattern 12ft. 15ft. 30ft. Trim Loss 1 0 1 10 ft. 2 4 0 3 8 4 5 STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established: 2 2 Min s.t. 4 3 0 1 3 Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12) + 1(15) + 2(30) = 99 feet used resulting in 100-99 = 1 foot of trim loss). Orders in hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. Any of the three types the open market at the selling price. No inventory is held. Pattern (a) Formulate an integer programming model that will determine how many 100-foot rolls to cut into each of the five…Friendly Waste Co. runs three different factories and is required by law to safely dispose of chemicals. Waste from three different factories can be processed to reduce the amount of two different types of pollutants. State law requires that the total reduction in the amount of pollutant A is at least 30 tons and pollutant B is at least 40 tons. Using the information in the following table: Factory Proc Cost Per Ton Reduction Plant A Reduction Plant B 1 15 0.1 0.45 2 10 0.2 0.25 3 20 0.4 0.3 •Algebraically formulate a linear programming model to represent this problem.
- Problem 7-41 Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oil. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery used to produce the gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons. a. Formulate linear programming model that can be used to determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize tota profit contribution. If required, round your answers to two decimal places. L Let R = P =…The following is a L.P.P: Max 10.3X1 -3.6X2 + 12X3 (Hundreds of dollars $) 5.t: (production capacity; hours) (warehouse capacity; hundreds of sq. ft.) X1 + X2 + 2X3 0 The optimal solution to the model as follows: Basis Cij 10.3X1 -3.6X2 12X3 OS1 OS2 OS3 RHS -1 18 S1 X1 X3 1 -1 11 10.3 1 1 -1 1 1 12 C-Z How much is the Absolut value of the reduced cost (in $) in the optimal solution? i.e Absolut value of |-5| = always = 5