CB 2011 Final Exam
Please submit it through Canvas on time!
Q1. (30 marks) Western Clothing Company produces two types of jeans, with the
limitations of the three resources: cloth, cutting time and sewing time. In general, the
monthly sales demand x of a type of jeans relates to its unit selling price p as follows:
? = ? - ? ∗ ? where a and b are parameters.
Table 1 shows the values of a and b for each of the two types of jeans.
Table 1.
Jean Type 1 2
a 2300 4500
b 18.6 19.8
Table 2 shows the per-jeans consumption rates of cloth, cutting time and sewing time
for each of the two types of jeans.
Table 2.
Jean Type 1 2
Cloth (in yard) 2.5 3.8
Cutting Time (in
minutes)
3.5 3.6
Sewing Time (in
minutes)
7.89 5.43
Table 3 shows the monthly availabilities of cloth, cutting time and sewing time.
Table 3.
Cloth 8500 yards
Cutting time 9500 minutes
Sewing time 19,500 minutes
a. What are the maximum unit selling prices of the two types of jeans, so that negative
monthly sales demands of the jeans can be avoided? Give your answers with two
decimal points. (8 marks)
b. By incorporating the results in (a), formulate a nonlinear programming model (in
terms of unit selling prices of the two types of jeans) for this problem to determine the