DSC3702
Optimisation of
Resources
, MEMO DSC3702 MAY 2018 DSC3702
This paper consists of 9 pages. 1 May/June 2018
Question 1
An operations manager is trying to determine a production plan for the next week. There
are three products (say, P, Q, and R) to produce using four machines (say, A, B, C and D).
Each of the four machines performs a unique process.
There is one machine of each type, and each machine is available for 2 400 minutes per
week. The unit processing times for each machine is given in Table 1.
Table 1: Machine Data
Unit Processing Time (min)
Machine Product P Product Q Product R Availability (min)
A 20 10 10 2 400
B 12 28 16 2 400
C 15 6 16 2 400
D 10 15 0 2 400
Total processing time 57 59 42 9 600
The unit revenues and maximum sales for the week are indicated in Table 2. Storage from
one week to the next is not permitted.
The material currently available is worth R80 000.
Table 2: Product Data
Item Product P Product Q Product R
Revenue per unit R900 R1 000 R700
Material cost per unit R450 R400 R200
Profit per unit R450 R600 R500
Maximum sales 100 40 60
Formulate an LP to determine the amount of each product that should be manufactured
during the present week in order to maximize profits.
[10]
Let P denote the number of unite of product P produced.
Let Q denote the number of unite of product Q produced.
Let R denote the number of unite of product R produced.
Maximise profit = 450P + 600Q + 500R
Page 1 of 9
Optimisation of
Resources
, MEMO DSC3702 MAY 2018 DSC3702
This paper consists of 9 pages. 1 May/June 2018
Question 1
An operations manager is trying to determine a production plan for the next week. There
are three products (say, P, Q, and R) to produce using four machines (say, A, B, C and D).
Each of the four machines performs a unique process.
There is one machine of each type, and each machine is available for 2 400 minutes per
week. The unit processing times for each machine is given in Table 1.
Table 1: Machine Data
Unit Processing Time (min)
Machine Product P Product Q Product R Availability (min)
A 20 10 10 2 400
B 12 28 16 2 400
C 15 6 16 2 400
D 10 15 0 2 400
Total processing time 57 59 42 9 600
The unit revenues and maximum sales for the week are indicated in Table 2. Storage from
one week to the next is not permitted.
The material currently available is worth R80 000.
Table 2: Product Data
Item Product P Product Q Product R
Revenue per unit R900 R1 000 R700
Material cost per unit R450 R400 R200
Profit per unit R450 R600 R500
Maximum sales 100 40 60
Formulate an LP to determine the amount of each product that should be manufactured
during the present week in order to maximize profits.
[10]
Let P denote the number of unite of product P produced.
Let Q denote the number of unite of product Q produced.
Let R denote the number of unite of product R produced.
Maximise profit = 450P + 600Q + 500R
Page 1 of 9
