QMI1500 Assignment 02 Semester 01 2020 Answers

QMI1500
Elementary Quantitative Methods
Assignment 01 for Semester 01 (compulsory)
Unique Number 839368

Preview of Question 1

The study shows that the demand (number of units sold) for a new product is 1 100
units per week when priced at R350, and 850 units per week when priced at R400.
Let 𝑥 represent the price of the product and 𝑦 the demand per week. Assume that
the relationship between the price and demand is linear and that the demand is
dependent on the price. The linear equation you could use to predict the demand for
other prices, is

1. 𝑦 = −50𝑥 + 350.
2. 𝑦 = −5𝑥 + 2850.
3. 𝑦 = 150𝑥 + 850.
4. 𝑦 = −5𝑥 + 450.
Answer:
1 100 units per week @ R350
850 units per week @ R400
𝑥 = Price of the product
𝑦 = Demand per week
𝑦 = 𝑎𝑥 + 𝑏
𝑦2−𝑦1
𝑎= 𝑥2−𝑥1
850−1 100
𝑎= 𝑅400−𝑅350
−250
𝑎= 𝑅50

𝑎 = −5
Therefore:
𝑦 = −5𝑥 + 6
And 1 100 = −5(𝑅350) + 6
= −5 × 𝑅350 + 6
= −1 750 + 6

, Add 1750 on both sides:

1 100 + 1 750 = −1 750 + 1750 + 6
2850 = 𝑏
Therefore:
𝑦 = −5𝑥 + 2850