Question

1. LG Company produces three types of parts for automatic vacuum machines. It purchases castings of the parts from a local foundry and then finishes the part on drilling, shaping and polishing machines. The selling prices of parts A, B, and C respectively are Php 80, Php 100 and Php140. All parts made can be sold. Castings for parts A, B and C respectively cost Php50, Php60 and Php100. The shop possesses only one of each type of machine. Cost per hour to run each of the three machines are Php200 for drilling, Php300 for shaping and Php300 for polishing. The capacities (parts per hour) for each part on each machine are shown in the following table.

                       

                                                            Capacities Per Hour

                           Machine        Part A               Part B              Part C

                        Drilling                25                     40                    25

                        Shaping               25                     20                     20

                        Polishing             40                     30                     40

      The management of the shop wants to know how many parts of each type it should produce per hour in order to maximize profit for an hour’s run. Formulate this problem as an LP model so as to maximize total profit to the company.

Answer 1

1. Let X1, X2 and X3 be the number of types A, B and C parts produced per hour respectively.

2. With the information given, the hourly profit for part A, B, and C would be as follows:

Profit per type A part = (80 – 50) – (200/25 +300/25 + 300/40) = 2.5

Profit per type B part = (100 – 60) – (200/40 + 300/20 + 300/30) = 10

Profit per type C part = (140 – 100) – (200/25 + 300/20 + 300/40) = 9.5

Then, Maximize Z = 2.5 X1 + 10 X2 + 9.5 X3

3. The above objective function is subjected to following constraints:

i) The drilling machine constraint X1/25 + X2/40 + X3/25 ≤ 1

ii) The shaping machine constraint X1/25 + X2/20 + X3/20 ≤1

iii) The polishing machine constraint X1/40 + X2/30 + X3/40 ≤1

X1, X2, X3 ≥ 0

Answer 2

An electronic company produces three types of parts for automatic machines. it purchases casting of the parts from the local foundry and then finishes parts on drilling, shaping and polishing machines. the selling price of parts A, b, and C respectively are Birr 18,10,14. All parts made can be sold. casting for parts A, B and C respectively costs Birr 5,6 and 10. the shop possesses only one of each type of machine. costs per hour to run each of the three machines are Birr 20 for drilling, 30 for shaping, and 30 for polishing.  Capacity per hour for each part are Part A, B, and C drilling 25,40,25 respectively.

The capacities (part per hour) for each part on each machine are in the table formulate this problem as an LP model so as to maximize total profit to the company.

capacity per hour for shaping part A, B and C are 25,20 and 20 respectively. and also, capacity per hour for polishing part A, B, and C are40,30 and40 respectively.