2.1)
Here, Given Data,
Capacity of the Machine M-100 = 25 Printer cases per Hour,
Capacity of the Machine M -200 = 40 printer cases per Hour,
Material Usage for the machine M-100 = 40 Pounds per Hour
Material Usage for the machine M-200 = 50 Pounds per Hour
The Given cost for the raw material = USD 6 per Pound,
X1 = Number of Hours spent on the Machine -100
X2 = Number of Hours spent on the Machine -200,
Again, Total cost = Cost of Raw Material X Number of Pounds Material usage
Or, 6*40*X1 +6*50*X2 + 50*X1 + 75*X2 = 290*X1 + 375*X2
Again Total Revenue = 25*18*X1 + 40*18*X2 = 450*X1 + 720*X2,
Profit would be Total Revenue minus Total Cost
Or, profit = (450*X1 + 720*X2) – (290*X1 + 375*X2) = 160*X1 + 345*X2,
We will be Maximizing Z or Profit Value,
So, Objective Function is Maximizing Z = 160*X1 + 345*X2,
Decision Variables are X1 and X2,
Constraints or subject to:
For Downtime case,
for the Machine M -100, X1=< 15,
for the Machine M -200, X2=< 10,
for high setup cost,
for the machine M -100, X1>= 5,
For the Machine M-200, X2>=5,
Considering Raw Material, Constraint 40*X1 + 50*X2 =< 1000
X1, X2>=0(Non-negativity)
2.2)
The optimum solution,
When X2 = 10, X1 will be 12.5,
Calculation: 40*X1 + 50X2 = 1000, or, 40*X1 + 50*10 = 1000, or, 40*X1 = 500, or, X1 = 12.5,
Here, optimal point is X1 = 12.5 and X2 = 10,
2.3)
Now Maximizing the Profit or Z = 160*X1 + 345*X2 = 160*12.5 + 345*10 = 5450 or USD 5450,
Now let me calculate slack time for each constraints:
If X1 =< 15, then Slack time would be 15 – 12.5 = 2.5 Hours
If X2 =<10, then Slack time would be 10 – 10 = Zero Hours
If X1 >=5, then Slack time would be 15 – 5 = 10 Hours
If X2 >=5, then Slack time would be 10 – 5 = 5 Hours
Kindly Upvote if Helpful :)
HOPE THIS MAY HELP YOU----------------------
------------------------------THANK
YOU---------------------------
2 Jackson Hole Manufacturing Jackson Hole Manufacturing is a small manufacturer of plastic products used in the automotive and computer industries. One of its major contracts is with a large computer...
Jackson Hole Manufacturing is a small manufacturer of plastic products used in the automotive and computer industries. One of its major contracts is with a large computer company and involves the production of plastic printer cases for the computer companys portable printers. The printer cases are produced on two injection molding machines. The M-100 machine has a production capacity of 25 printer cases per hour, and the M-200 machine has a production capacity of 40 cases per hour. Both machines...
Input Prices Direct materials Plastic Metal Direct manufacturing labor $ 6 per pound $ 5 per pound $ 12 per direct manufacturing labor hour Input Quantities per Unit of Output Cat-allac Dog-eriffic Direct materials Plastic Metal Direct manufacturing labor-hours (DMLH) Machine-hours (MH) 5 pounds 0.5 pounds 3 hours 12 MH 7 pounds 1 pound 5 hours 20 MH Inventory Information, Direct Materials Metal Beginning inventory Target ending inventory Cost of beginning inventory Plastic 220 pounds 400 pounds 924 70 pounds...
Scannell Industries manufactures a variety of custom products. The company has traditionally used a plantwide manufacturing overhead rate based on machine hours to allocate manufacturing overhead to its products. The company estimates that it will incur $1,695,000 in total manufacturing overhead costs in the upcoming year and will use 15,000 machine hours. Click the icon to view the additional information about the hazardous waste disposal fees.) Expected usage and costs for manufacturing overhead activities for the upcoming year are as...
Preble Company manufactures one product. Its variable manufacturing overhead is applied to production based on direct labor-hours and its standard cost card per unit is as follows: $ 45 42 24 Direct material: 5 pounds at $9 per pound Direct labor: 3 hours at $14 per hour Variable overhead: 3 hours at $8 per hour Total standard variable cost per unit $ 111 The company also established the following cost formulas for its selling expenses: Fixed Cost Variable Cost per...
Concord Manufacturing Company, a small manufacturer of appliance parts, has just completed its first year of operations. The company's controller, Kenneth Clark has been reviewing the results for the year and is concerned about the application of factory overhead. Trainor is using the following information to assess operations. • Concord uses several machines with a combined cost of $2,250,000 and no residual value. Each machine has an output of 5 units of product per hour and a useful life of...
Preble Company manufactures one product. Its variable manufacturing overhead is applied to production based on direct labor-hours and its standard cost card per unit is as follows: Direct materials: 5 pounds at $10 per pound $ 50 Direct labor: 4 hours at $14 per hour 56 Variable overhead: 4 hours at $4 per hour 16 Total standard cost per unit $ 122 The planning budget for March was based on producing and selling 29,000 units. However, during March the company...
please full calculation and explanation
Containers, Inc. produced 62,500 and sold 59.000 plastic microcomputer cases at a selling price on 10.00 each. Manufacturing overhead is allocated on the basis of machine hours. The standard variable costs Per computer case were: Total Quantity Rate Direct Materials 1.5 kg $ 1.20 per kg $1.80 Direct Labour 0.50 labour hours $ 15.00 per hour 7.50 Variable Overhead 0.20 machine hours $ 6.00 per hour 1.20 Information regarding fixed overhead includes the following: Budgeted...
Preble Company manufactures one product. Its variable manufacturing overhead is applied to production based on direct labor-hours and its standard cost card per unit is as follows: $ 0.00 Direct material: 5 pounds at $8.00 per pound Direct labort 3 hours at $15 per hour Variable overhead: 3 hours at 59 per hour Total standard variable cost per unit The company also established the following cost formulas for its selling expenses. Variable Cost per Unit Sold Advertising Sales salaries and...
Preble Company manufactures one product. Its variable manufacturing overhead is applied to production based on direct labor-hours and its standard cost card per unit is as follows: Direct material: 5 pounds at $8.00 per pound Direct labor: 2 hours at $14 per hour Variable overhead: 2 hours at $5 per hour Total standard variable cost per unit $40.00 28.00 19.00 $78.00 The company also established the following cost formulas for its selling expenses: Variable Cost per Unit Sold Fixed Cost...
Preble Company manufactures one product. Its variable manufacturing overhead is applied to production based on direct labor-hours and its standard cost card per unit is as follows: Direct material: 6 pounds at $8.00 per pound $ 48.00 Direct labor: 4 hours at $17 per hour 68.00 Variable overhead: 4 hours at $4 per hour 16.00 Total standard variable cost per unit $ 132.00 The company also established the following cost formulas for its selling expenses: Fixed Cost per Month Variable...