CPI manufactures a standard dining chair used in restaurants. The dema quarter 2
ID: 357140 • Letter: C
Question
CPI manufactures a standard dining chair used in restaurants. The dema quarter 2 are 3700 and 4200, respectively. The chair contains an uphostereauced a new prices of S13.75 ef purchased from DAP. DAP currently charges $12.25 per seat, but has ann$10.25 per scat. Seats seat that can be prod quarter 1 and by CPI the second quarter. CPI can produce at most 3800 seats per quarter 13.75 effective seat cost C.P si.s each to hold in order to satisfy demand in quamnerimal make or buy plan for CPL (15 pes at a cost o t cost CPI $1.50 nventory, and maximum inventory cannot exceed 300 seats. Find the The problem is formulated as follows: X1 = Number of seats produced by CPI in quarter 1. Number of seats purchased from DAP in quarter 1 x,-Number of seats carried in inventory from quarter 1 to 2. X, = Number of seats purchased from DAP in quarter 2. The linear programming model is provided next Subject to: XNumber of seats produced by CPI in quarter 2. Minimize l 0.25x,+12.5x,+1.5Xs+10.25x,+13.75x, X,+ X2-3700+ X, X,+ X+x5-4200 X,33800 x, 300 ?, x2, x, x, and X5 are non-negative The linear programming model was run using SOLVER and the output results are given below: Final Reduced Objective Allowable Allowable Decrease Cell Name Value Cost Coefficient Increase 10.25 1E+30 0.25 1E+ 1000 3800 0 3000 10.25 3.5 SES2 X4 SFS2 X5 (a) What is the optimal solution including the optimal value of the objective function? (5 pts) (b) If the per-unit inventory cost increased from $1.50 to $2.50, would the optimal solution change? Please esplain it. (Please refer to the table above and information below.) (10 ps) Objective Allowable Allowable Coefficient Increase Decrease 0.25 Lower bound 1.5-0.25 1.25 Upper bound 1.5 + 23.5Explanation / Answer
a)
optimal solution is as given:
X1 = 3800
X2 = 0
X3 = 100
X4 = 3800
X5 = 300
optimal value of objective function:
10.25*3800 + 12.5*0 + 1.5*100 + 10.25*3800 + 13.75*300
= 38950 + 0 + 150 + 38950 + 4125
= 82175
b) if the inventory cost is increased from 1.5 to 2.5 the optimal solution will not change.
Since the allowable increase is 2, the upper bound as calculated is 3.5, hence inventory cost can increase upto 3.5 yet the solution will remain the same. Hence if it increases to 2.5 the solution will not change.