Ramona bowen was employed as a supervisor for comfort manufacturing. she was the only black supervisor in the plant. the other s
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<h3>Explanation:</h3><h3>Part (a):</h3>
Solved part is attached as an image.
<h3>Part (b):</h3>Let us first determine the amount required of each item to produce 1 bracket.
From the attached diagram, we can see that to manufacture 1 bracket, quantity of each item needed is,
Base = 1
Spring = 2
Clamp = 1 + 4 = 5
Housing = 2
Handle = (1 * 1) + (4 * 1) = 5
Casting = (1 * 1) + (4 * 1) = 5
Bearing = 2 * 2 = 4
Shaft = 2 * 1 = 2
Hence, for 50 Brackets, quantity of each item required will be,
Base = 1 * 50 = 50
Spring = 2 * 50 = 100
Clamp = 5 * 50 = 250
Housing = 2 * 50 = 100
Handle = 5 * 50 = 250
Casting = 5 * 50 = 250
Bearing = 4 * 50 = 200
Shaft = 2 * 50 = 100
<em>NOTE: The above quantities give exclusive quantities required for each item. In actual practice, we won't have to purchase base, clamp & housing separately as the will be assembled from their components which are already procured.</em>
<h3>Part (c):</h3>As 25 bases are already in stock, parts for them will not be needed. I will refer the quantities subtracted due to this by indicating (B). Similarly, quantities subtracted due to clamps will be indicated as (C).
Base = 50 - 25 = 25
Spring = 50
Clamp = 250 - 100 - 25(B) = 125
Housing = 100 - (2*25)(B) = 50
Handle = 1 * 125 = 125
Casting = 1 * 125 = 125
Bearing = 2 * 50 = 100
Shaft = 1 * 50 = 50
Answer:
a.
Look at the two attached figures please. The decision variables is the choice to build a fire station in which city.
So there are six decision variables each taking a value of either 0 or 1.
D1 = decision to build fire station in city 1, (1 denotes yes and 0 denotes no)
D2 = decision to build fire station in city 2, (1 denotes yes and 0 denotes no)
D3 = decision to build fire station in city 3, (1 denotes yes and 0 denotes no)
D4 = decision to build fire station in city 4, (1 denotes yes and 0 denotes no)
D5 = decision to build fire station in city 5, (1 denotes yes and 0 denotes no)
D6 = decision to build fire station in city 6, (1 denotes yes and 0 denotes no)
b.
Please look at attachment
C .
The figure 1 denotes the problem formulation in excel and shows all the formulas.
In first step, a matrix is prepared to denote all cities which are within 15 minutes by 1 and others by zero
A array of decision variables for selecting the city is shown. A 1 in cell implies that city is selected and 0 means the city is not selected.
A product of the selection variable and the value in the within 15 minutes matrix is calculated as shown by the formula.
The constraint is to ensure that all cities have at least one fire station mapped within 15 minutes.
d.
The problem is solved in Excel using integer programming and the solution is that City 2 and 4 should be selected for building fire stations and thus total no of fire stations are two with every city within 15 minutes.
Explanation:
