Question

2. A company manufactures 3 products a, b and c, which sells $ 14, $15 and $22 per unit respectively. These prices are constant and independent of the market state they are addressed to, and it is also supposed that any produced quantity can be sold. For the manufacturing of these products four types of raw materials are required. The prices of raw materials, the raw material units needed for each product type and the corresponding available quantities within a certain time period are included in the following table. Raw Unit price The raw material units needed for Available raw material of raw each product type material units materials Product Product Product a b c 1 3 0 2 3 50 2 2 3 2 1 200 3 0.5 4 4 6 200 4 1 0 0 2 100 The company's goal is to determine the quantities of each product which should be produced in order to achieve the highest profit. Define in detail the decision variables and form the objective function and all constraints of the problem. Formulate a linear programming model that can be used to determine the quantities of each product which should be produced in order to achieve the highest profit. (Do NOT need to find the optimal solution. You just need to form the linear programming model.) (10 marks)

          2. A company manufactures 3 products a, b and c, which sells $ 14, $15 and $22 per
unit respectively. These prices are constant and independent of the market state they
are addressed to, and it is also supposed that any produced quantity can be sold. For
the manufacturing of these products four types of raw materials are required. The
prices of raw materials, the raw material units needed for each product type and the
corresponding available quantities within a certain time period are included in the
following table.
Raw
Unit price
The raw material units needed for Available raw
material
of raw
each product type
material units
materials
Product
Product
Product
a
b
c
1
3
0
2
3
50
2
2
3
2
1
200
3
0.5
4
4
6
200
4
1
0
0
2
100
The company's goal is to determine the quantities of each product which should be
produced in order to achieve the highest profit.
Define in detail the decision variables and form the objective function and all
constraints of the problem. Formulate a linear programming model that can be used
to determine the quantities of each product which should be produced in order to
achieve the highest profit. (Do NOT need to find the optimal solution. You just
need to form the linear programming model.) (10 marks)

2. A company manufactures 3 products a, b and c, which sells 14,15 and 22 per
unit respectively. These prices are constant and independent of the market state they
are addressed to, and it is also supposed that any produced quantity can be sold. For
the manufacturing of these products four types of raw materials are required. The
prices of raw materials, the raw material units needed for each product type and the
corresponding available quantities within a certain time period are included in the
following table.
Raw
Unit price
The raw material units needed for Available raw
material
of raw
each product type
material units
materials
Product
Product
Product
a
b
c
1
3
0
2
3
50
2
2
3
2
1
200
3
0.5
4
4
6
200
4
1
0
0
2
100
The company's goal is to determine the quantities of each product which should be
produced in order to achieve the highest profit.
Define in detail the decision variables and form the objective function and all
constraints of the problem. Formulate a linear programming model that can be used
to determine the quantities of each product which should be produced in order to
achieve the highest profit. (Do NOT need to find the optimal solution. You just
need to form the linear programming model.) (10 marks)

Added by Veronica H.

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