A factory manufactures three products, A, B, and C. Each product requires the use of two machines,Machine I and Machine II. The total hours available, respectively, on Machine I and Machine Il per month are6,450 and 9,700. The time requirements and profit per unit for each product are listed below.A BCMachine I 5 9 7Machine II 9 9 14$10 $16 $22ProfitHow many units of each product should be manufactured to maximize profit, and what is the maximumprofit?Start by setting up the linear programming problem, with A, B, and C representing the number of units ofeach product that are produced.Maximize P =subject to:s 6,450s 9,700Enter the solution below. If needed round numbers of items to 1 decimal place and profit to 2 decimalplaces.The maximum profit is $when the company produces:units of product Aunits of product Bunits of product C

Objective Functions and Constraints: Based on the given details, the objective…

Answered: A factory manufactures three products,…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 111P

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The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
12. A company has limited material (10,000 kg) and labour (2,000 hours) for the coming period and is using linear programming to determine the optimal production plan. Details of its two products are as follows: Product Material (£2 per kg) Labour (£20 per hour) Fixed overhead per unit Profit per unit Selling price Original budgeted production 3,000 2,000 Let: q = number of product Q made r = number of product R made. What is the objective function? (a) 40q+ 25r (b) 26q+14r (c) 10q + 9r (d) 14q+ 11r 6 20 10 40 R£40295 10 25
The Ace Manufacturing Company has orders for three similar products. Product A Min B C 1 2 Machine 3 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A A B B Ic C Product 1 12 3 Orders (units) 1,900 500 1,100 Capacity (units) 1,300 1,600 800 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20 (a) Develop the linear programming formulation of this problem. (Let XA1 be the number of units of product A produced by machine 1, X;; be the number of units of product i produced by machine j, etc.)
Because of its labor contract, a company must hire enough labor for 100 units ofproduction per week on one shift or 200 units per week on two shifts. It cannot hire,lay off, or assign overtime. During the fourth week, workers will be available fromanother department to work part or all of an extra shift (up to 100 units). There is aplanned shutdown for maintenance in the second week, which will cut production tohalf. Develop a production plan. The opening inventory is 200 units, and the desiredending inventory is 300 units
Cox Electric makes electronic components and has estimated the following for a new design of one of its products. Fixed cost = $23,750 Material cost per unit = $0.17 • Labor cost per unit = $0.12 • Revenue per unit = $0.67 Note that fixed cost is incurred regardless of the amount produced. Per-unit material and labor cost together make up the variable cost per unit. Assuming that Cox Electric sells all that it produces, profit is calculated by subtracting the fixed cost and total variable cost from total revenue. Construct an appropriate spreadsheet model to find the profit based on a given production level and use the spreadsheet model to answer these questions. (a) Construct a one-way data table with production volume as the column input and profit as the output. Breakeven occurs when profit goes from a negative to a positive value; that is, breakeven is when total revenue = the total cost, yielding a profit of zero. Vary production volume from 0 to 100,000 in increments of 10,000.…
1. Cox Electric makes electronic components and has estimated the following for a new design of one of its products. Fixed cost = $24,375 Material cost per unit = $0.17 Labor cost per unit = $0.12 Revenue per unit = $0.68 Note that fixed cost is incurred regardless of the amount produced. Per-unit material and labor cost together make up the variable cost per unit. Assuming that Cox Electric sells all that it produces, profit is calculated by subtracting the fixed cost and total variable cost from total revenue. Construct an appropriate spreadsheet model to find the profit based on a given production level and use the spreadsheet model to answer these questions. a. Construct a one-way data table with production volume as the column input and profit as the output. Breakeven occurs when profit goes from a negative to a positive value; that is, breakeven is when total revenue = the total cost, yielding a profit of zero. Vary production volume from 0 to 100,000 in increments of 10,000.…
Direct Materials and Direct Labor Variance Analysis Shasta Fixture Company manufactures faucets in a small manufacturing facility. The faucets are made from brass. Manufacturing has 50 employees. Each employee presently provides 32 hours of labor per week. Information about a production week is as follows: Standard wage per hour $12.00 Standard labor time per unit 15 min. Standard number of lbs. of brass 1.5 lbs. Standard price per lb. of brass $11.00 Actual price per lb. of brass $11.25 Actual lbs. of brass used during the week 11,124 lbs. Number of units produced during the week 7,200 Actual wage per hour $12.36 Actual hours for the week (50 employees × 32 hours) 1,600 Required: a. Determine the standard cost per unit for direct materials and direct labor. Round the cost per unit to two decimal places. Direct materials standard cost per unit $fill in the blank 1 Direct labor standard cost per unit $fill in the blank 2 Total standard cost per unit $fill in…
A company has limited machine hours available per week, in result the company is able to produce only 3 of 4 products. The company needs to increase the number of hours worked using the existing machinery by working overtime. Such overtime would be paid at a premium of 50% above normal labour rates, and variable overhead costs would be expected to increase in proportion to labour costs. Critically discuss any expected increase in contribution and any issues (in particular in regard to overtime working) that could arise and would need to be resolved. What would be advantages and disadvantages of that and how this will affect the quanitity and the quality of the production and the whole process.
Manufacturing Aggregate Planning Manufacturers Inc. (MI) currently has a labor force of 10, which can produce 600 units per period. The labor cost is now $5000 per period per employee. The company has a long-standing rule that does not allow it to make use of any overtime. In addition, the product cannot be subcontracted, due to the specialized nature of the machinery that MI uses to produce it. As a result, MI can only increase/decrease production by hiring or laying off employees. The cost is $10000 to hire or lay off an employee. Inventory carrying costs are $200 per unit for any unsold items at the end of the period. The inventory level at the beginning of period 1 is 400 units. The forecast demand is 700 in period 1,600 in period 2,450 in period 3, 250 in period 4,500 in period 5, and 550 in period 6. a.) Compute the costs of the Chase Demand Strategy. b.) Compute the costs of the Level Strategy c.) Compare the costs of the two strategies. Which one is superior?
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A company produces three products A,B, and C. The products are processed through three machines as follows Standard Standard Standard ProductAnnual demand Time on m/c 1Time on m/c 2Time on m/c 3 A 600 15 350 2 1000 12 10 If there are 250 working days per year and the company plans to work one seven hours shift per day, then compute the number of machines required. B.

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