A. Francophone is a telecommunication company, which is located in the Accra – Adabraka. The company sells mobile phones and accessories. Most of their newly released phones are ordered. Francophone stocks three main phones for walk-in customers. Every week, they generate profits of GH¢600 from selling Galaxy S2, GH¢400 from Galaxy S3 and GH¢300 from Galaxy S4. The overall weekly cost of these types of phones are GH¢1,800, GH¢2,100 and GH¢1,200 respectively. This week, Francophone has a budget of GH¢12,000 available to buy these three types of phones. During sales, each phone type must be unpacked, leading to 8 hours of unpacking time for S2 phones, 12 hours for S3 phones and 16 hours for S4 phones. The manager estimates that he and his workers have 120 labour hours available to unpack the three types of phones. He has enough space to order 20 phones this week. The manager also wants to stock at least twice as many S4 as S2 and S3 phones because S4 phones sell better. 2 a) Formulate a linear programming model for this problem. B. Use the table below to answer the following questions. Table 1: Solver Output Variable cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$9 Galaxy S2 3 0 600 1E+30 290.91 -$B$10 Galaxy S3 0 -320 400 320 1E+30 $B$11 Galaxy S4 6 0 300 900 600 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $F$4 budget LHS 9000 0 12000 1E+30 3000 $F$5 labour LHS 120 30 120 40 120 $F$6 space LHS 9 0 20 1E+30 11 $F$7 mix LHS 0 180 0 10 7.5 b) Determine the minimum profit for Galaxy S3 so that it will attain a positive value in the optimal solution. c) Explain with reasons why reduce cost for galaxy3 is negative. d) If Francophone could raise their budget by GH¢1,500 per week or increase the weekly hours to 150, which should it choose? Advice. With reasons.
Question 1
A. Francophone is a telecommunication company, which is located in the Accra –
Adabraka. The company sells mobile phones and accessories. Most of their newly
released phones are ordered. Francophone stocks three main phones for walk-in
customers. Every week, they generate profits of GH¢600 from selling Galaxy S2,
GH¢400 from Galaxy S3 and GH¢300 from Galaxy S4. The overall weekly cost of these
types of phones are GH¢1,800, GH¢2,100 and GH¢1,200 respectively.
This week, Francophone has a budget of GH¢12,000 available to buy these three types of
phones. During sales, each phone type must be unpacked, leading to 8 hours of unpacking
time for S2 phones, 12 hours for S3 phones and 16 hours for S4 phones. The manager
estimates that he and his workers have 120 labour hours available to unpack the three types
of phones. He has enough space to order 20 phones this week. The manager also wants to
stock at least twice as many S4 as S2 and S3 phones because S4 phones sell better.
2
a) Formulate a linear programming model for this problem.
B. Use the table below to answer the following questions.
Table 1: Solver Output
Variable cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$9 Galaxy S2 3 0 600 1E+30 290.91
-$B$10 Galaxy S3 0 -320 400 320 1E+30
$B$11 Galaxy S4 6 0 300 900 600
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$F$4 budget LHS 9000 0 12000 1E+30 3000
$F$5 labour LHS 120 30 120 40 120
$F$6 space LHS 9 0 20 1E+30 11
$F$7 mix LHS 0 180 0 10 7.5
b) Determine the minimum profit for Galaxy S3 so that it will attain a positive value in the
optimal solution.
c) Explain with reasons why reduce cost for galaxy3 is negative.
d) If Francophone could raise their budget by GH¢1,500 per week or increase the weekly
hours to 150, which should it choose? Advice. With reasons.
Step by step
Solved in 2 steps with 2 images
