Question

Group Ex #5 (Ch 10)

A manufacturing company has a pool of 50 labor hours. A customer has requested two products, Product A and Product B, and has requested 15 and 20 of each respectively. It requires 2 hours of labor to produce Product A and 3 hours of labor to produce Product B. The company can obtain up to 50 additional hours of labor if required. In-house labor costs $25 per hour while contracted labor costs $45 per hour.

A- Draw the network flow model that captures this problem.

B-Write out the LP formulation for this problem?

C-Solve this system – the network flow problem. [Provide a screen shot of your Solver solution and/or any Solver Reports you deem necessary.]

D-What is the company’s labor plan to develop the products, A and B, to fulfill the customer’s order?

(f) And, what is the associated cost to the company?

Answer 1

1) Network flow model is following

Supply (labor hours) Demand (labor hours $25 50 Inhouse Labor Product A 15x2 30 $45 $25 50 Contracted labor Product B20x3 -60 $45

2) LP formulation is as follows

Let HA and HB be the number of inhouse labor hours used to produce products A and B respectively

and CA and CB be the number of contracted labor hours used to produce products A and B respectively

Min (HA+HB)*25 + (CA+CB)*45

s.t.

HA+HB <= 50

CA+CB <= 50

HA/2 + CA/2 = 15

HB/3 + CB/3 = 20

HA, HB, CA, CB >= 0

3) Solution of the model using Solver is as follows

F2 Q fx -SUMPRODUCT (B2:E2,$B$8:$E$8) HB св S Solver Parameters 2 3 4 5 6 Cost: Supply of Inhouse labor Supply of Contracted labor Demand A Demand B 25 Set Objective SFS2l O Max Min O Value of: 0 0.5 0.5 15 15 By Changing Variable Cells: 0.33 0.33 SBS8 SES Subject to the Constraints: 8 Result: 30 10 Add 10 Change 12 13 14 15 16 17 18 19 Delete Reset AI Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the IPOPT Nonlinear engine for Solver Problems that are smooth nonlinear.Select the LP Simplex engine for linear Solver Problems. 21 23 Solve dose 25

Formula:

F2 =SUMPRODUCT(B2:E2,$B$8:$E$8)   copy to F2:F6

Solver Answer report is following

Objective Cell (Min Cell Name Original Value Final Value SF$2 Cost: 3050 3050 Variable Cells Cell SB$8 Labor hours to be used: HA $C$8 Labor hours to be used: HB $D$8 Labor hours to be used: CA SE$8 Labor hours to be used: CB Name Original Value Final Value Integer 50 30 10 0 Contin 50 Contin 30 Contin 10 Contin Constraints Cell $F$3 Supply of Inhouse labor $F$4 Supply of Contracted labor SF$5 Demand A SF$6 Demand B Name Cell Value Formula Status Slack 50 $F$3<-SH$3 Binding 40 SF$A<-SH$4 Not Binding 15 ŞF$5-$H$5 Bindin 20 SF$6-SH$6 Binding 10

4)

Company's labor plan is such that 50 inhouse labor hours should be used for producing B and 30 and 10 contracted labor hours should be used for production of A and B respectively.

Associated cost to the company = $ 3050