A company produces three different types of wrenches: W111, W222 and W333. It ha
ID: 3537656 • Letter: A
Question
A company produces three different types of wrenches: W111, W222 and W333. It has a firm order for 2,000 W111 wrenches, 3750 W222 wrenches and 1700 W33 wrenches. Between now and the order delivery data, the company has only 16,500 fabrication hours and 1,600 inspection hours. The time that each wrench requires in each department is shown in the table below. Also shown are the costs to manufacture the wrenches in-house and the costs to outsource them. For labeling considerations, the company wants to manufacture in-house at least 60% of each type of wrench that will be shipped. We need to determine how many wrenches of each type should be made in-house and how many should be outsourced. Also, we will determine the total cost to satisfy the order.
1. First, what are the decision variables?
The table below lists the time that each wrench requires in each department and the costs to manufacture wrenches in-house and costs to outsource them.
Wrench
Fabrication Hours
Inspection Hours
In-House Cost
Outsource Cost
W111
2.5
0.25
$ 17.00
$ 20.40
W222
3.4
0.30
$ 19.00
$ 21.85
W333
3.8
0.45
$ 23.00
$ 25.76
2. Using the problem from question 4, what is the objective function? Provide a brief explanation of how you defined it.
3. Using the problem from question 4, what are your constraints? Provide a brief explanation of how you analyzed the problem to define your constraints.
A company produces three different types of wrenches: W111, W222 and W333. It has a firm order for 2,000 W111 wrenches, 3750 W222 wrenches and 1700 W33 wrenches. Between now and the order delivery data, the company has only 16,500 fabrication hours and 1,600 inspection hours. The time that each wrench requires in each department is shown in the table below. Also shown are the costs to manufacture the wrenches in-house and the costs to outsource them. For labeling considerations, the company wants to manufacture in-house at least 60% of each type of wrench that will be shipped. We need to determine how many wrenches of each type should be made in-house and how many should be outsourced. Also, we will determine the total cost to satisfy the order.
1. First, what are the decision variables?
The table below lists the time that each wrench requires in each department and the costs to manufacture wrenches in-house and costs to outsource them.
Wrench
Fabrication Hours
Inspection Hours
In-House Cost
Outsource Cost
W111
2.5
0.25
$ 17.00
$ 20.40
W222
3.4
0.30
$ 19.00
$ 21.85
W333
3.8
0.45
$ 23.00
$ 25.76
2. Using the problem from question 4, what is the objective function? Provide a brief explanation of how you defined it.
3. Using the problem from question 4, what are your constraints? Provide a brief explanation of how you analyzed the problem to define your constraints.
Explanation / Answer
In any linear programming problems first we have to identify below things
You need to identify these concepts when formulating linear programming models.
The first step when formulating a model is to identify and give names to the decision variables. Decision variables are the elements of the model that the decision maker controls and those values determine the solution of the model.
The next step is to determine the objective function in terms of the decision variables. The objective function is where you specify the goal you are trying to achieve. The goal can either be to maximize or to minimize the value of the objective function. We sometimes use the phrase that we want to optimize the model. This means we want to find the values for the decision variables which gives either the maximum or the minimum value of the objective function. In many cases, the objective function has a monetary value, for example to maximize profit or minimize cost, although this is not always the case.
Constraints are the real world limitations on the decision variables. A constraint restricts or constrains the possible values which the variable can take. An example of a constraint could be, for example, that certain resources, such as machine capacity or manpower, are limited.
in this problem
Fabrication Hours
Inspection Hours
In-House Cost
Outsource Cost
are the descison variables
Objective function are
$ 17.00 x+
$ 20.40y = 2000
$ 19.00x +
$ 21.85y =3750
Fabrication Hours
Inspection Hours
In-House Cost
Outsource Cost
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