LINEAR PROGRAMMING

Case Study

A company produce three type of electric components - Resistance, Capacitor and Inductor whose selling price per unit are Rs. 5, 7 and 10 respectively. All the components can be sold. The cost of raw form resistance, capacitor and inductor are Rs. 3, Rs. 4 and Rs. 6 respectively. Before selling these components, the company is required to polish, charge and shape them. The company possesses only of each type of machine. Cost per hour to run each of the three machines are Rs. 15 for polishing, Rs. 20 for charging and Rs. 25 for shaping. The capacities (parts per hour) for each part on each machine are shown in the following table.

Capacity per hour

Machine Resistance Capacitor Inductor

Polishing 35 25 30

Charging 15 30 30

Shaping 50 45 40

If x_1, x_2 and x_3 denotes the number of each type product to be produced per hour, answer the following question based on the problem above.

Question 1: Combined profit of the company from all three components to be maximised is _________

a. 0.26 x_1 + 1.17 x_2 + 2.2 x_3

b. 2 x_1 + 2.42 x_2 + 2.68 x_3

c. 2.2 x_1 + 0.26 x_2 + 1.17 x_2

d. None of these

Q 2 Constraint of the problem on the avaialability of charging machine is ________

a. x_1/25 + x_2/30 + x_3/45 less than or equal to 1

b. x_1/15 + x_2/30 + x_3/30 less than or equal to 1

c. 15/x_1 + 30/x_2 + 30/x_3 less than or equal to 1

d. x_1/15 + x_2/30 + x_3/30 less than 1

Q 3 Constraint of the problem on the avaialability of polishing machine is ________

a. x_1/35 + x_2/15 + x_3/50 less than or equal to 1

b. 35/x_1 + 25/x_2 + 30/x_3 less than or equal to 1

c. x_1/35 + x_2/25 + x_3/30 less than or equal to 1

d. x_1/35 + x_2/25 + x_3/30 less than 1

Q 4 Constraint of the problem on the avaialability of shaping machine is ________

a. x_1/30 + x_2/30 + x_3/40 less than or equal to 1

b. x_1/15 + x_2/45 + x_3/40 less than or equal to 1

c. 30/x_1 + 30/x_2 + 40/x_3 less than or equal to 1

d. x_1/15 + x_2/45 + x_3/40 less than 1

Q 5 Total cost of manufacturing per unit of capacitor is _____

a. 3.79

b. 7.6

c. 6

d. 8

Q 6 Total cost of manufacturing per unit of inductor is _____

a. 6.79

b. 7.32

c. 7

d. 8

Q 7 Total cost of manufacturing per unit of resistance is _____

a. 5.26

b. 4

c. 2

d. 5

Q 8 Total profit per unit of capacitor is ______

a. 2.42

b. 0.5

c. 2

d. 1

Q 9 Total profit per unit of inductor is ______

a. 2.68

b. 2.2

c. 3

d. None of these

Q 10 Total profit per unit of resistence is ______

a. 0.26

b. 0.37

c. 2

d. 4