Please, i need a complete answer. From Q(a). to (c). thanks.
Question 1 Telefonika is a telecommunication company, located in the Accra Mall, selling mobile phones and accessories. Most of their new phones are ordered. But, Telefonika stocks three main phones for walk-in customers. Every week, they generate profit of GHC600 from selling Galaxy S2, GHC400 from Galaxy S3 and GHC300 from Galaxy S4. The overall weekly cost of these types of phones are GHC1,800, GHC2,100 and GHC1,200 respectively. This week, Telefonika has a budget of GHC12,000 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 54 phones. The manager estimates that he and his workers have 120 labour hours available to unpack the three types of phones. Telefonika has enough space to order 20 phones this week. The manager also wants to stock at least twice as many S4 as S2 and 53 phones because S4 phones sell better. a) Formulate a linear programming model for this problem. AP(10 marks) b) The model was solved using excel solver and part of the results provided in table 1 below. Use it to answer the questions that follow. (i) What is the optimal solution for Telefonika's problem? (ii) Determine the total weekly profit that Telefonika makes? (iii) Which resource constraint(s) are binding? Give a reason. (iv) If Telefonika could raise its budget by GHC1,500 per week or increase the weekly hours to 150, which should it choose and why? AN(5 marks) c) (i) Which resource is not fully utilized? Justify your answer. (ii) If Telefonika's profit per unit from Galaxy S4 phones was GHC200 instead of GHC300, how could that affect the optimal solution? How could that affect profit? (iii) What is the minimum profit for Galaxy S3 so that it will attain a positive value in the optimal solution? AN (5 marks) Table 1: Solver Output 2 Table 1: Solver Output 2 Variable cells Reduce Cell $B$9 $B$10 $B$11 Name Galaxy S2 Galaxy S3 Galaxy S4 Reduce Final d Valu e Cost 3 0 0 -320 6 0 Allowabl Allowabl Objective e e Coefficie Decreas nt Increase e 600 1E+30 290.91 400 320 1E+30 300 900 600 Constrain ts e Shado Final w Valu e Price Constrain Allowabl Allowabl t Decreas R.H. Side Increase Cell $F$4 9000 0 12000 1E+30 3000 Name budget LHS labour LHS space LHS mix LHS 30 $F$5 $F$6 $F$7 120 9 0 0 120 20 0 40 1E+30 10 120 11 7.5 180 TOTAL:20Marks Question 1 Telefonika is a telecommunication company, located in the Accra Mall, selling mobile phones and accessories. Most of their new phones are ordered. But, Telefonika stocks three main phones for walk-in customers. Every week, they generate profit of GHC600 from selling Galaxy S2, GHC400 from Galaxy S3 and GHC300 from Galaxy S4. The overall weekly cost of these types of phones are GHC1,800, GHC2,100 and GHC1,200 respectively. This week, Telefonika has a budget of GHC12,000 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 54 phones. The manager estimates that he and his workers have 120 labour hours available to unpack the three types of phones. Telefonika has enough space to order 20 phones this week. The manager also wants to stock at least twice as many S4 as S2 and 53 phones because S4 phones sell better. a) Formulate a linear programming model for this problem. AP(10 marks) b) The model was solved using excel solver and part of the results provided in table 1 below. Use it to answer the questions that follow. (i) What is the optimal solution for Telefonika's problem? (ii) Determine the total weekly profit that Telefonika makes? (iii) Which resource constraint(s) are binding? Give a reason. (iv) If Telefonika could raise its budget by GHC1,500 per week or increase the weekly hours to 150, which should it choose and why? AN(5 marks) c) (i) Which resource is not fully utilized? Justify your answer. (ii) If Telefonika's profit per unit from Galaxy S4 phones was GHC200 instead of GHC300, how could that affect the optimal solution? How could that affect profit? (iii) What is the minimum profit for Galaxy S3 so that it will attain a positive value in the optimal solution? AN (5 marks) Table 1: Solver Output 2 Table 1: Solver Output 2 Variable cells Reduce Cell $B$9 $B$10 $B$11 Name Galaxy S2 Galaxy S3 Galaxy S4 Reduce Final d Valu e Cost 3 0 0 -320 6 0 Allowabl Allowabl Objective e e Coefficie Decreas nt Increase e 600 1E+30 290.91 400 320 1E+30 300 900 600 Constrain ts e Shado Final w Valu e Price Constrain Allowabl Allowabl t Decreas R.H. Side Increase Cell $F$4 9000 0 12000 1E+30 3000 Name budget LHS labour LHS space LHS mix LHS 30 $F$5 $F$6 $F$7 120 9 0 0 120 20 0 40 1E+30 10 120 11 7.5 180 TOTAL:20Marks
