Question 1
Fixed cost = R6,000; Cost per item = R80; Selling price = R200. Find total revenue, total cost, and
profit function.
Correct Answer: a
Working:
Total Revenue: TR = 200q
Total Cost: TC = 80q + 6000
Profit: π = TR − TC = 200q − (80q + 6000) = 120q − 6000
Question 2
Fixed cost = R12,000; Variable cost = R300; Selling price = R600. Find the break-even quantity.
Correct Answer: c
Working:
Break-even occurs when TR = TC
600q = 300q + 12000
300q = 12000
q = 40
Question 3
Fixed cost = R8,000; Cost per unit = R200; Selling price = R400. If the company made a loss of
R4,000, how many units were sold?
Correct Answer: a
Working:
π = TR − TC = 400q − (200q + 8000) = 200q − 8000
Loss of R4,000 means π = −4000
200q − 8000 = −4000
, 200q = 4000
q = 20
Question 4
If P = 25 − 0.01x and C = 10000 + 5x, find TR and profit functions.
Correct Answer: a
Working:
TR = P × x = (25 − 0.01x)x = 25x − 0.01x2
π = TR − TC = (25x − 0.01x2 ) − (10000 + 5x) = −0.01x2 + 20x − 10000
Question 5
If P = 4.00 and C = 400 + 2x, find the break-even quantity.
Correct Answer: a
Working:
TR = 4x
TC = 400 + 2x
Break-even: 4x = 400 + 2x
2x = 400
x = 200
Question 6
Profit function: y = −3x2 + 18x − 10. Approximately how many units must be produced to
maximise profit?
Correct Answer: a
Working:
b 18 18
Maximum occurs at vertex: x = − 2a
= − 2(−3)
= − −6
=3
, Question 7
Find equilibrium price and quantity given:
Pd = 500 − 6Qd , Ps = 4Qs + 20
Correct Answer: a
Working:
At equilibrium: Qd
= Qs = Q and Pd = Ps
500 − 6Q = 4Q + 20
480 = 10Q
Q = 48
P = 500 − 6(48) = 500 − 288 = 212
Question 8
Find equilibrium P and Q rounded to integers, given:
Pd = −Q2 + 9Q + 11, Ps = Q2 − 3Q + 29
Correct Answer: a
Working:
At equilibrium: −Q2 + 9Q + 11 = Q2 − 3Q + 29
−Q2 + 9Q + 11 − Q2 + 3Q − 29 = 0
−2Q2 + 12Q − 18 = 0
Divide by -2: Q2 − 6Q + 9 = 0
(Q − 3)2 = 0
Q=3
P = −9 + 27 + 11 = 29
Question 9
Given P = 60 − 3Q, find elasticity at P = 30.
Correct Answer: a
Fixed cost = R6,000; Cost per item = R80; Selling price = R200. Find total revenue, total cost, and
profit function.
Correct Answer: a
Working:
Total Revenue: TR = 200q
Total Cost: TC = 80q + 6000
Profit: π = TR − TC = 200q − (80q + 6000) = 120q − 6000
Question 2
Fixed cost = R12,000; Variable cost = R300; Selling price = R600. Find the break-even quantity.
Correct Answer: c
Working:
Break-even occurs when TR = TC
600q = 300q + 12000
300q = 12000
q = 40
Question 3
Fixed cost = R8,000; Cost per unit = R200; Selling price = R400. If the company made a loss of
R4,000, how many units were sold?
Correct Answer: a
Working:
π = TR − TC = 400q − (200q + 8000) = 200q − 8000
Loss of R4,000 means π = −4000
200q − 8000 = −4000
, 200q = 4000
q = 20
Question 4
If P = 25 − 0.01x and C = 10000 + 5x, find TR and profit functions.
Correct Answer: a
Working:
TR = P × x = (25 − 0.01x)x = 25x − 0.01x2
π = TR − TC = (25x − 0.01x2 ) − (10000 + 5x) = −0.01x2 + 20x − 10000
Question 5
If P = 4.00 and C = 400 + 2x, find the break-even quantity.
Correct Answer: a
Working:
TR = 4x
TC = 400 + 2x
Break-even: 4x = 400 + 2x
2x = 400
x = 200
Question 6
Profit function: y = −3x2 + 18x − 10. Approximately how many units must be produced to
maximise profit?
Correct Answer: a
Working:
b 18 18
Maximum occurs at vertex: x = − 2a
= − 2(−3)
= − −6
=3
, Question 7
Find equilibrium price and quantity given:
Pd = 500 − 6Qd , Ps = 4Qs + 20
Correct Answer: a
Working:
At equilibrium: Qd
= Qs = Q and Pd = Ps
500 − 6Q = 4Q + 20
480 = 10Q
Q = 48
P = 500 − 6(48) = 500 − 288 = 212
Question 8
Find equilibrium P and Q rounded to integers, given:
Pd = −Q2 + 9Q + 11, Ps = Q2 − 3Q + 29
Correct Answer: a
Working:
At equilibrium: −Q2 + 9Q + 11 = Q2 − 3Q + 29
−Q2 + 9Q + 11 − Q2 + 3Q − 29 = 0
−2Q2 + 12Q − 18 = 0
Divide by -2: Q2 − 6Q + 9 = 0
(Q − 3)2 = 0
Q=3
P = −9 + 27 + 11 = 29
Question 9
Given P = 60 − 3Q, find elasticity at P = 30.
Correct Answer: a
