Set up an L.P. model to maximize the profit. Solve the L.P. model by simplex method.
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A firm manufactures three products A, B and C. The profits are K3, K2 and K4 respectively. The firm has two machines and the required processing time in minutes for each machine on each product is given below.
Machine |
Product |
||
A |
B |
C |
|
X |
4 |
3 |
5 |
Y |
2 |
2 |
4 |
Machines X and Y have 2,000 and 1,500 machine – minutes respectively. The firm must manufacture 100 A’s, 200 B’s and 50 C’s but no more than 150 A’s
- Set up an L.P. model to maximize the profit.
- Solve the L.P. model by simplex method.
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- A company has one machine which can be used to make product Alpha and product Beta. Each unit of product Alpha requires 45 minutes of machine time, while each unit of product Beta requires 37 minutes of machine time. The machine can be used for 8 hours per day and 5 days per week. Next week the company will produce 23 units of product Alpha. After completing the production of Alpha, the company will produce product Beta. How many units of product Beta can be produced next week? Use at least 4 decimals.You must showm your calculation steps and brief explanation on your Excel spreadsheets.fi Auto mobile company manufactures cars and trucks. Each vehicle must be processed in the paint shop and body assembly shop. If the paint shop were only painting trucks, then 80 per day could be painted. If the paint shop were only painting cars, then 120 per day could be painted. If the body shop were only producing cars, then it could process 100 per day. If the body shop were only producing trucks, then it could process 100 per day. Each truck contributes GHS60,000 to profit, and each car contributes GHS40,000 to profit. Use linear programming to determine a daily production schedule that will maximize the company’s profits.FRUIT COMPUTER COMPANY Fruit Computer Company manufactures memory chips in batches of ten chips. From past experience, Fruit knows that 80% of all batches contain 10% (1 out of 10) defective chips, and 20% of all batches contain 50% (5 out of 10) defective chips. If a good (that is, 10% defective) batch of chips is sent to the next stage of production, processing costs of $4000 are incurred, and if a bad batch (50% defective) is sent on to the next stage of production, processing costs of $16000 are incurred. Fruit also has the alternative of reworking a batch at a cost of $4000. A reworked batch is sure to be a good batch. Alternatively, for a cost of $400, Fruit can test one chip from each batch in an attempt to determine whether the batch is defective. QUESTIONS 1.Determine a strategy so Fruit can minimize the expected total cost per batch. 2.Compute the EVSI and EVPI.
- A machine part to be fabricated may be made from alloy of either of two metals. There is an order for 10,000 units. Metal A costs 3 pesos per kg, while Metal B costs 9 pesos per kg. If Metal A is used, the material per unit weighs 110 grams; for metal B, 30 grams. When metal A is used, 50 units can be produced per hour; for metal B, 80 units per hour. Metal B fabrication requires the aid of a tool costing P1,000, which will be useless after the 10,000 units are finished. The machine operator's wage is P50 per hour. If all other costs are identical, determine which material will be more economical to finish the 10,000-unit order. How much is the total cost difference between the use of metal A and metal B?A small firm makes three similar products, which all follow the same three-step process, consisting of milling, inspection, and drilling. Product A requires 12 minutes of milling, 5 minutes forinspection, and 10 minutes of drilling per unit; product B requires 10 minutes of milling, 4 minutesfor inspection, and 8 minutes of drilling per unit; and product C requires 8 minutes of milling, 4minutes for inspection, and 16 minutes of drilling. The department has 20 hours available duringthe next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes$2.40 per unit to profit, product B contributes $2.50 per unit, and product C contributes $3.00 perunit. Determine the optimal mix of products in terms of maximizing contribution to profits for theperiod. Then, find the range of optimality for the profit coefficient of each variable.A manufacturing plant produces a product 'A' that requires one unit of 'B' and ½ unit of 'C'. Each unit of 'B' is comprised of one unit of 'D', two units of 'E', and one unit of 'F'. Each unit of 'C' requires ½ unit of 'G' and three units of 'H'. The manufacturing lead times for the components are as follows: 'A' - two weeks, 'B' - one week, 'C' - two weeks, 'D' - two weeks, 'E' - three weeks, 'F' - one week, 'G' - two weeks, 'H' - one week. There are 20 units in stock for each of these components. 100 units of 'A' are needed for delivery in seven weeks: a) Develop the product structure and indexed bill of materials for the product. b) Create a gross and net requirements plan for the manufacturer of the product.
- Susan Williams runs a small Flagstaff job shop where garments are made. The job shop employs eight workers. Each worker is paid $8 per hour. During the first week of March, each worker worked 40 hours. Together, they produced a batch of 132 garments. Of these garments, 54 were 'seconds' (meaning that they were flawed). The seconds were sold for $90 each at a factory outlet store. The remaining 78 garments were sold to retail outlets at a price of $200 per garment. What was the labor productivity, in dollars per labor-hour, at this job shop during the first week of March? Labor productivity = dollars/labor hour (round your response to two decimal places).Green Vehicle Inc. manufactures electric cars and small delivery trucks. It has just opened a new factory where the C1 car and the T1 truck can both be manufactured. To make either vehicle, processing in the assembly shop and in the paint shop are required. It takes 1/40 of a day and 1/60 of a day to paint a truck of type T1 and a car of type C1 in the paint shop, respectively. It takes 1/50 of a day to assemble either type of vehicle in the assembly shop. A T1 truck and a C1 car yield profits of $300 and $220, respectively, per vehicle sold. a) Define the objective function and constraint equations. b) Graph the feasible region. c) What is a maximum-profit daily production plan at the new factory? d) How much profit will such a plan yield, assuming whatever is produced is sold?4) The making of rivet holes in structural steel members can be done by 2 methods. The first method consists of laying out the position of the holes in the members and using a drill press costing P100k. The machinist is paid P60 per hour and he can drill 80 holes per hour. The second method makes use of a multiple-punch machine costing P80k. The punch operator is paid P40 an hour and he can punch out 1 hole for 3 seconds. This method also requires an expense of P1.25 per hole to set the machine. (a) if all other costs are assumed equal, what is the total cost for each machine for 10k holes, assuming the total cost of each machine to be charged to these holes? (b) for how many holes will the costs be equal?
- A company that operated 10 hours a day manufactures two products on three sequential processes. The following table summarizes the data for the problem: Product Process 1 10 Process 2 20 Process 3 8 10 Unit Profit 20 30 Which of the following is the most appropriate representation for variables x and y for the given situation? x is the # of units of Product 1 to be procured; y is the # of units of Product 2 to be procured. x is the # of units of Product 1 to be stored; y is the # of units of Product 2 to be stored x is the # of units of Product 1 to be delivered, y is the # of units of Product 2 to be delivered. x is the # of units of Product 1 to be produced; y is the # of units of Product 2 to be produced. minutesSusan Williams runs a small Flagstaff job shop where garments are made. The job shop employs eight workers. Each worker is paid $8 per hour. During the first week of March, each worker worked 45 hours. Together, they produced a batch of 156 garments. Of these garments, 54 were 'seconds' (meaning that they were flawed). The seconds were sold for $100 each at a factory outlet store. The remaining 102 garments were sold to retail outlets at a price of $198 per garment. What was the labor productivity, in dollars per labor-hour, at this job shop during the first week of March? Labor productivity =______ dollars/labor hour (round your response to two decimal places). Please don't just send the answer, I need to know how to do this. Thanksgreen vehicule Inc. manufactures electric cars and small delivery trucks. it has just opened a new factory where the C1 car and the T1 truck can both be manufactured. to make either vehicle, processing in the assembly shop and the paint shop are required. It takes 1/40 of a day and 1/60 of a paint a truck of type T1 and a car of type C1 in the paint shop, respectively. it takes 1/50 of a day to assemble either type of vehicule in the assembly shop. A t1 truck and a C1 car yield profits of $300 and $220, respectively, per vehicule sold