PT Bangun Industri Persada (BIP) manufactures five different products in any combination. Each product requires time on each of three machines, as shown in the following table. All figures are in minutes per pound (lb) of product.

Product	Machine-Time (Min/Lb)
	1	2	3
A	12	8	5
B	7	9	10
C	8	4	7
D	10	0	3
E	7	11	2

Each machine is available 128 hours per week. Products A, B, C, D, and E are purely competitive, and any amounts made may be sold at per pound prices of $5, $4, $5,$4, and $4, respectively. Variable labor costs are $ 4 per hour for machines 1 and 2, and $3 per hour for machine 3. Material costs are $2 for each pound of products A and C, and $1 for each pound of products B,D, and E. BIP wish to maximize profit to the firm. The contribution margins of products A,B,C, D, and E per pound produced are $1.417, $1.433, $1.850, $2.183, and $1.7, respectively. Use the LP solution and Sensitivity Report shown below to answer the following:

1. Write a complete LP Model for this problem.
2. Find the optimal solution. (how many pounds should each product be produced?)
3. How many hours are spent on each of the three machines?
4. How much should the firm be willing to spend to obtain another hour of time on machine 2?
5. How much can the sales price of product A increase before the optimal production plan changes? State your answer in the proper units.

 

HI B A $5 $4 $4 $3 $2 E 1 Product 2 Price/Lb. 3 Cost/Hr Mach. 1 4 Cost/Hr Mach. 2 5 Cost/Hr Mach. 3 6 Matrl.Costs//Lb 7 Product 8 Pounds Prod. 9 Contr. Mar./Lb 10 |11 Mach. 1 Min. 12 Mach. 2 Min. 13 Mach. 3 Min. 14. E $5 $4 $4 $3 $2 $4 $4 $4 $3 $1 $4 $4 $4 $4 $3 $1 $4 $4 $3 $1 A Mach. Hours AvailWeek 512 512 Profit 128 $1.417 $1.433 $1.850 $2.183 $1.700 $ 1,817.60. Total 7680 < 7680 s 4608 < Min.Avail.Wk. Slack 7E-07 2E-08 3072 12 7 8 10 7 7680 8 9. 4 11 5 7680 7680 10 F82-SUMPRODUCT(83 B5,811:B13)60-B6; Copied to C9:F9 Microsoft Excel 8.0 Sensitivity Report Adjustable Cells Cell SB$8 Pounds Prod. A $C$8 Pounds Prod. B $D$8 Pounds Prod. C SE$8 Pounds Prod. D $F$8 Pounds Prod. E Constraints Final Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 1E+30 1E+30 0.041 1E+30 0.081 Name Value 1.380 0.245 0.093 -1.380 -0.245 1.417 1.433 512 1.85 2.183 -0.075 0.075 512 1.700 0.1125 Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease Cell Name $G$11 Mach. 1 Min. Total $G$12 Mach. 2 Min. Total $G$13 Mach. 3 Min. Total 7680 7680 4608 2671.304 2792.727 4388.571 1E 30 0.2258 0.0108 7680 7680 7680 3840 3072