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 are 6,450 and 9,700. The time requirements and profit per unit for each product are listed below. A BC Machine I 5 9 7 Machine II 9 9 14 $10 $16 $22 Profit How many units of each product should be manufactured to maximize profit, and what is the maximum profit? Start by setting up the linear programming problem, with A, B, and C representing the number of units of each product that are produced. Maximize P = subject to: | s 6,450 s 9,700 Enter the solution below. If needed round numbers of items to 1 decimal place and profit to 2 decimal places. The maximum profit is $ when the company produces: units of product A units of product B units of product C
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- 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.)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 25Because 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?The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor utilization, and product profitability: Department A B C 1.00 0.30 0.20 Profit contribution/unit $30.00 Production Labor-Hours Required (a) Develop a linear programming model of the Hartman Company problem. Solve the model to determine the optimal production quantities of products 1 and 2. If required, round your answer to two decimal places. Product 1 Product 2 (hours/unit) Product 1 Product 2 Hours Available OT hours: (b) In computing the profit contribution per unit, management does not deduct labor costs because they are considered fixed for the upcoming planning period. However, suppose that overtime can be scheduled in some of the departments. Which departments would you recommend scheduling for overtime? - Select your answer - What is the upper limit of what you would be willing to pay…
- The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor utilization, and product profitability: Labor-Hours Required Department A B с (hours/unit) Product 1 Product 2 Hours Available Production 1.00 0.30 Profit contribution/unit $30.00 0.20 38.27 0.35 0.20 0.50 $15.00 (a) Develop a linear programming model of the Hartman Company problem. Solve the model to determine the optimal production quantities of products 1 and 2. If required, round your answer to two decimal places. Product 1 Product 2 69.77 M 95 72.09 38 50 (b) In computing the profit contribution per unit, management does not deduct labor costs because they are considered fixed for the upcoming planning period. However, suppose that overtime can be scheduled in some of the departments. Which departments would you recommend scheduling for overtime? Dept A What is the upper limit of what…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.11. Shown below are the planning period's demand and the standard hours required for four products from a company's sales and operations plan. Assume that the company has 65,000 hours of labor available during the planning period, and determine whether the sales and operations plan is feasible. Product Units Demanded Standard Hours (in hours/unit) A 32,500 0.60 B 23,000 0.80 0 40,000 0.20 D 15,000 1.15