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DSC1520 Exam Revision May/June Past Papers & Answers 2026 |Quantitative Modelling I|

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Institution
University Of South Africa
Course
Quantitative Modelling I

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DSC1520: Quantitative Modelling I

May/June Examination 2026 — Revision Guide


⋆ ⋄ ⋆ ⋄ ⋆ ⋄ ⋆ ⋄ ⋆

Mathematics for Economics and Business




Exam Revision Guide


DSC1520
Module Code:
Quantitative Modelling I
Module Name:
May/June 2023 - May/June 2025
Papers Covered:
May/June Examination 2026
Focus Year:
100 marks (2 Hours)
Total Marks:
Programmable calculator permitted
Calculator:



Questions sourced from UNISA DSC1520 past papers (2023–2024). Work through

each answer step by step. Focus on understanding, not memorisation.




Exam Revision Notes | DSC1520 | 2026

,DSC1520 | Exam Revision May/June Examination 2026



PART 1: DSC1520 — May/June 2024 Examination
100 Marks | 2 Hours | Programmable Calculator Permitted




Page 2 of 30

, DSC1520 | Exam Revision May/June Examination 2026



Question 1 [20 marks]




(a) [8 marks]




Question: The demand and cost functions for a commodity are given by:


P = 40 − 0.2Q and C(Q) = 1 000 + 15Q


where P is the price per unit and Q is the quantity produced and sold.

(i) Determine the profit function π(Q). [2]
(ii) Find the break-even quantity (or quantities). [3]
(iii) Find the quantity that maximises profit, and state the maximum profit. [3]


Answer: (i) Profit function:
Total Revenue = P × Q = (40 − 0.2Q) Q = 40Q − 0.2Q2


π(Q) = T R − T C = (40Q − 0.2Q2 ) − (1 000 + 15Q)

π(Q) = −0.2Q2 + 25Q − 1 000

(ii) Break-even quantity:
Set π(Q) = 0:
−0.2Q2 + 25Q − 1 000 = 0

Multiply through by −5:
Q2 − 125Q + 5 000 = 0

Using the quadratic formula:
p √
125 ± 1252 − 4(1)(5 000) 125 ± 15 625 − 20 000
Q= =
2 2

∆ = 15 625 − 20 000 = −4 375 < 0




Page 3 of 30
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Quantitative Modelling I
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