MCQ Questions

Question No. 1

Solve the following inequalities. Represent each solution on a number line.

Answer :

g) 3x + 15 < 5 − 2x

a) 5x > 10

b) x − 4 < 2

c) −x ≤ 3

d) −7x ≥ 1

e) 8x + 3 > 19

f) 6 − 2x ≥ −4

h) 7x − 9 > 3x − 1

Question No. 2

Solve the following compound inequalities. Represent each solution on a number line.

Answer :

a) −1 < x < 5

b) 0 < 3x ≤ 9

c) 5 ≤ 2x + 1 < 7

d) −4 ≤ 2 + 3x ≤ 17

e) 4 ≥ −x > 3

f) 16 < −2x ≤ 8

g) −5 ≤ 2 − 7x ≤ 16

h) −12 > 6 − 9x ≥ 15

Question No. 3

Sketch the graph and shade the region that contains the solution for each of the following inequalities.

Question No. 4

Sketch the graphs and shade the region that contains the solution for each of the following pairs of inequalities. Label each line with its inequality, as shown in the examples.

Answer :

a) −5x + 3y ≤ 15 and 3x + 6y ≥ −18

b) 7x + 2y < 14 and x + 4y > −4

c) −2x + 5y > 10 and 3x + y ≥ 6

d) −2x + y ≤ 2 and 3x + 2y < −9

e) −5x + 6y ≤ 30 and 7x + y ≥ −7

f) 5x + 4y ≥ 20 and x + y < 5

Question No. 5

Sketch the graphs and shade the region that contains the solution for each of the following sets of inequalities. Write each inequality next to its line.

Answer :

a) 3x + 5y ≤ 15, −2x + 3y ≥ −6 and x ≥ 1

b) 6x + 5y < 30, −x + y ≤ 4 and y > 2

c) x + y ≤ 3, −x + y > −3 and x ≥ −1

d) 2x + 7y < 14, x ≥ 0 and y ≥ 0

e) −x + y ≥ −2, 2x + y > −2 and y < 5

f) −4x + 3y ≤ 12, y ≥ 0 and x < 2

Question No. 6

Write down all the constraints for each situation in the form of inequalities.

Answer :

a) A factory makes tables and chairs: at most 100 items each week; at least 10 tables; for each table at least four chairs. Let x = tables, y = chairs.

Write the inequalities.

b) A farmer plants cassava and yams on 50 ha: at least 10 ha cassava; at least 15 ha yams; no crop more than 60% of land. Let x = cassava ha, y = yams ha.

Write the inequalities.```

Question No. 7

Solve:

Answer :

a) A factory makes tables and chairs. The factory can make at most 100 items each week. The factory must make at least 10 tables every week. For each table, there must be at least four chairs. Let x be the number of tables and y be the number of chairs that the factory must make. Write down all the constraints for this situation in the form of inequalities.

b) A farmer produces two main crops: cassava and yams. She has 50 hectares of farmland on which she can plant her crops. She is contracted to plant at least 10 hectares under cassava and at least 15 hectares under yams. She does not want to plant more than 60% of her farmland under any one crop. Let x and y be the number of hectares that she plants under cassava and yams respectively. Write down all the constraints for this situation in the form of inequalities.

Question No. 8

Given the inequalities x ≥ 10, y ≥ 0, x + y ≤ 100 and y ≥ 4x.

Answer :

a) Graph these inequalities on a sheet of graph paper.

b) Shade the feasible region.

Question No. 9

Given the inequalities x + y ≤ 50, x ≥ 10, y ≥ 15, x ≤ 30 and y ≤ 30.

Answer :

a) Graph these inequalities on a sheet of graph paper.

b) Shade the feasible region.

Question No. 10

Find the coordinates of the vertices labelled A, B and C of the feasible region shown in this diagram.

Answer :

Question No. 11

Find the coordinates of the vertices labelled A, B, C, D and E of the feasible region shown in this diagram.

Answer :

Question No. 12

A factory makes x tables and y chairs every week. Formulate the objective function for each of the following scenarios.

Answer :

a) If it takes 9 hours to make a table and 7 hours to make a chair, express the total working hours (M) required per week in terms of x and y.

b) If the cost of making a table is ₦140 000 and the cost of making a chair is ₦95 000, express the total weekly cost (C) in terms of x and y.

c) If the profit on one table is ₦65 000 and the profit on one chair is ₦42 000, express the total weekly profit (P) in terms of x and y.

Question No. 13

A farmer plants x hectares of farmland under cassava and y hectares under yams. Formulate the objective function for each of the following scenarios.

Answer :

a) If it takes five labourers to harvest one hectare of cassava and 30 labourers to harvest 1 hectare of yams, express the total number of labourers (L) required in terms of x and y.

b) If one hectare of cassava yields 18 tonnes and 1 hectare of yams yields 30 tonnes, express the total number of tonnes (T) that will be harvested in terms of x and y.

Question No. 14

A feasible region has these vertices: A(0; 0), B(0; 160) and C(50; 125). Find the maximum and minimum values of each of the following objective functions.

Answer :

a) C = 98 000x + 69 000y, where C is the cost in naira

b) M = 40x + 60y, where M is the number of working hours required

c) A = 5x + 2.5y, where A is the storage space required in square metres

Question No. 15

A feasible region has these vertices: A(15; 25), B(15; 195), C(30; 170) and D(45; 115). Find the maximum and minimum values of each of the following objective functions.

Answer :

a) F = 800x + 750y, where F is the fuel required in litres

b) T = 20x + 35y, where T is the maintenance time in hours

c) M = 10x + 5y, where M is the mass in tonnes

Question No. 16

A brand of fruit juice is made from fresh mangoes and guavas. Every batch must contain at least 60 pieces of fruit, but not more than 90 pieces of fruit. The number of mangoes used must be at least twice, but not more than four times, the number of guavas used. Let x and y be the number of mangoes and guavas used respectively in one batch of juice.

Answer :

a) Write down all the constraints for this situation.

b) Graph the inequalities on a sheet of graph paper, shade the feasible region and label the vertices.

c) Find the coordinates of the vertices of the feasible region.

d) If mangoes cost ₦250 each and guavas cost ₦150 each, what number of each kind of fruit should be used to minimise the cost of making one batch of juice?

Question No. 17

A bicycle factory is revamping its assembly section. There is a choice of two types of assembly line. Type A can produce five bicycles per day. It occupies 40 m² of floor space and needs eight skilled workers to operate it. Type B can produce three bicycles per day. It occupies 60 m² of floor space, but needs only four skilled workers to operate it. There is a total amount of 480 m² of floor space available for the assembly lines. Only 64 skilled workers are available. Let x and y be the number

Answer :

a) Write down all the constraints for this situation.

b) Graph the inequalities on a sheet of graph paper, shade the feasible region and label the vertices.

c) Find the coordinates of the vertices of the feasible region.

d) If the objective is to produce the maximum number of bicycles per day, how many of each type of assembly line should be installed?

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