For a certain civil engineering system, it is sought to maximize the benefits, which is given by the expression: Z=3x+5y. The decision variables are x (the amount of resource type 1 to be used) and y (the amount of resource type 2 to be used). • The amount of resource type 1 should be at least 3 units. • The amount of resource type 2 should be at least 3 units. • The difference between the amount of resource type 2 and the amount resource type 1 should not exceed 6. • The total amount of resource types 1 and 2 should not exceed 12 units. a. Identify the obiective function for this problem. b. Identify and write the constraints. c. Provide a sketch graph for the constraint set. d. Clearly show the feasible region. e. Label all extreme points (or vertices) of the feasible region and indicate their coordinates. f. Solve the optimization problem.
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- The ore of a gold mine in the Itogon Benguet, on the average,1Kgram of gold per 10 ton. One method of processing costs P100,500 per ton and recovers 85% of the gold, while another methodcosts P200,000 per ton and recovers 90% of the gold. If gold can besolid at P2, 500 per gram, which method is better and by howmuch?#4- The mean number of air conditioning units assembled per month by Freeze, Inc. is 750 and the standard deviation is 100 units. a. If the number of air conditioning units assembled per month follows a normal distribution, calculate the probability of Freeze, Inc to assemble a quantity of air conditioning units greater than the monthly break-even point calculated in problem 3-a. b. An improved assembling process is proposed to Freeze, Inc. to reduce the variable cost from $500 per unit to $400 per unit., increase the mean number of air conditioning units assembled per month from 750 to 850 and reduce the standard deviation to 90 units. As a result of the improvements, monthly fixed costs would go up from $250,000 to $300,000. Once these improvements are implemented, calculate the new number of air conditioning units that Freeze Inc. must sell every month to break-even, discuss and justify if you would recommend the process improvement initiative. c. If the number of air conditioning…Northern Engineering is analyzing a mining project. Annual production, unit costs, and unit revenues are in the table. The first cost of the mine setup is $6 million. If MARR is 15%, what is the PW? Year Annual Production (tons) 90,000 120,000 120,000 100,000 80,000 60,000 40,000 Cost per ton $25 Price per ton $35 1 20 36 22 37 24 38 26 39 6. 28 40 7 30 41
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- please answer correctly. The selections are either BETA or ALPHA Mariah Enterprises makes a variety of consumer electronic products. Its camera manufacturing plant is considering choosing between two different processes, named Alpha and Beta, which can be used to make a component part. To make the correct decision, the managers would like to compare the labor and mulifactor produclivity of process Alpha wilth that of process Beta. The value of process oulput for Alpha and Beta is $130 per unit of product A and $200 per unit of product B, and the corresponding overhead costs for Alpha and Beta are $5,000 and $7,000, respectively. Process Alpha B Process Beta Product Output (units) Labor (S) Materials (S) A A B 40 60 80 50 $1,200 $1,400 $1,000 $2,000 $1,500 $2,500 S3,000 $3,500 a. Which process, Alpha or Beta, is more productive? Process has % higher labor productivity. Process V has % higher multifactor productivity. (Enter your responses rounded to the nearest whole number.)Kilmer Company's customer demand for its only product exceeds its manufacturing capacity. The company provided the following information for the machine whose limited capacity is prohibiting the company from producing and selling additional units: Actual run time this week Machine time available per week Actual run rate this week Ideal run rate Defect-free output this week Total output this week (including defects) 1-a. Utilization rate 1-b. Efficiency rate. 1-c. Quality rate 1-d. Overall equipment effectiveness 2-a. Utilization loss in units 2-b. Efficiency loss in units 2-c. Quality loss in units 23,310 minutes 25,900 minutes 0.90 8.00 units per minute 10 units per minute Required: 1. and 2. With respect to the company's overall equipment effectiveness, calculate the following: Note: Do not round intermediate calculations. Round final answers to 2 decimal places and "Units" answers to the nearest whole number. 149,184 units 186,480 unitsPrescribed fire is an important tool for foresters. A recent article describes how decision analysis is used to decide when, where and what to burn. In one example, a number of areas in the Tahoe National Forest in California had been logged and were being prepared for replanting. Preparation included prescribed burning, and two possible treatments were available: burning the slash as it lay on the ground, or “yarding of and merchantable material” (YUM) prior to burning. The latter treatment involves using heavy equipment to pile the slash. YUM reduces the difficulty of controlling the burn but costs an additional $100 per acre. In deciding between the two treatments two uncertainties were considered critical. The first was how the fire would behave under each scenario. For example, the buyer could be fully successful, problems could arise which could be controlled eventually, or the fire could escape entailing considerable losses. Second if problems developed, they could result in…
- Mazen is a ski resort manager who had to make a decision about adding another lift to this winter season. The decision was made depending on the accurate average snowfall of the previous 5 years. Mazen's decision was based on: * Certain environment O Risk environment Uncertain environment O Crisis environmentAqua Man Company manufactures and sells a single product. Planned and actual production in its first year of operation was 100,000 units. Planned and actual costs for the year were as follows: Manufacturing Non-manufacturing Variable P600,000 P500,000 Fixed P400,000 P300,000 The company sold 85,000 units of product at a selling price of P30 per unit. Using absorption costing, the company’s operating profit was Select one: a. P1,020,000 b. P975,000 c. P900,000 d. P750,000Case StudyThe ARCASNA company is dedicated to the manufacture of dog and cat food. Recently, the industrial engineering team became aware of potential areas of opportunity in the area of dog meat manufacturing. Currently, 45 liters of the solution are used to create them, and 50 jumbo, 75 medium and 100 small-sized chews are produced daily, to be sold and distributed in single packs (jumbo), trios (medium) and 5-packs (small). Recently there were inspections by the new manager in the industrial engineering area and the team realized that at the end of the day, among the "waste" (the material that remains at the end of each process), there is enough material left to fill a 5-liter bucket, which is wasted and thrown away. However, as there are 10 processes in total, there is very little left over at each of the stations, so they had never stopped to analyze the total loss per line. There are 6 workers on the line, distributed as follows: (Shown in the attached image). In addition, the…