PT Bangun lnclustri Persada {HIP} manufactures five different products in any combination. Each product requires time on each of three machines, as shown in the following table. ll figures are in minutes per pound [lb] of product. 1l'Iii'Iachine Time 2(Minbela Each machine is available 123 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, $554, and 54, respectively. 'v'ariable labor costs are S 4 per hourfor machines 1 and 2, and $3 per hour for machine 3. Material costs are 52 for each pound of products A and C. and $1 for each pound of products ELI}, and E. BIP wish to maximize profit to the firm. The contribution margins of products A,B,C, [3. and E per pound produced are 5141151433. 51.350.52.183. and 51?, respectively. Use the LP solution and Sensitivity Report shown below to answer the following: Write a complete LP Model for this problem. Find the optimal solution. [how many pounds should each product be produced?) El b c. How many hours are spent on each of the three machines? d How much should the firm be willing to spend to obtain another hour of time on machine 2? e. How much can the sales price of product A increase before the optimal production plan changes? State your answer in the proper units. B C m G H Product A B D E 2 Price/Lb $5 $4 $5 $4 3 Cost/Hr Mach. 1 $4 $4 $4 $4 $4 Cost/Hr Mach. 2 $4 $4 $4 $4 $4 5 Cost/Hr Mach. 3 $3 $3 $3 $3 $3 #6 Matrl.Costs/Lb $2 $1 $2 $1 $1 Product A B C D E Mach. Hours Avail/Week 8 Pounds Prod. 0 0 512 0 - 512 Profit 128 9: Contr. Mar./Lb $ 1.417 $1.433 $1.850 $2.183 $ 1.700 $ 1,817.60. 10 Total Min.Avail./Wk. Slack Mach. 1 Min. 12 10 7680 5 7680 7E-07 12 Mach. 2 Min. 11 7680 s 7680 2E-08 13 Mach. 3 Min. 10 2 4608