Upon leaving the shop, Kante buys orange juice and yoghurt for the family. If he earns €100 a week and the price of orange juice is €2 a carton, while yoghurt is priced at €4 a tub. What quantity will he be able to buy if he decides to all his income on e

To determine how much orange juice and yoghurt Kante can buy based on his weekly income of €100, we can calculate the maximum quantities of each item he can purchase if he spends all of his income on one commodity at a time. ### 1. **Buying Only Orange Juice:** - Price of orange juice: €2 per carton - Income: €100 To find out how many cartons Kante can buy if he spends all his money on orange juice, we divide his income by the price of a carton: \[ \text{Quantity of orange juice} = \frac{\text{Income}}{\text{Price per carton}} = \frac{100}{2} = 50 \text{ cartons} \] ### 2. **Buying Only Yoghurt:** - Price of yoghurt: €4 per tub - Income: €100 Now, we find out how many tubs of yoghurt he can buy if he spends all his money on yoghurt: \[ \text{Quantity of yoghurt} = \frac{\text{Income}}{\text{Price per tub}} = \frac{100}{4} = 25 \text{ tubs} \] ### 3. **Illustrating Kante’s Budget Constraint:** Kante’s budget constraint can be illustrated on a graph where: - The x-axis represents the quantity of orange juice (Q_oj). - The y-axis represents the quantity of yoghurt (Q_y). The intercepts of the budget constraint can be calculated as follows: - **When Kante buys only orange juice (x-intercept):** He can buy 50 cartons if he spends all his income on orange juice. - **When Kante buys only yoghurt (y-intercept):** He can buy 25 tubs if he spends all his income on yoghurt. The equation of the budget constraint can be represented as: \[ 2Q_{oj} + 4Q_y = 100 \] Rearranging this gives: \[ Q_y = 25 - 0.5Q_{oj} \] ### 4. **Graphing the Budget Constraint:** 1. **Plot the intercepts:** - (50, 0) where he buys only orange juice. - (0, 25) where he buys only yoghurt. 2. **Connect the points:** Draw a straight line between the intercept points, representing the various combinations of orange juice and yoghurt that Kante can buy with his €100 weekly income. ### **Conclusion:** Kante can buy a maximum of 50 cartons of orange juice or 25 tubs of yoghurt, and the graph illustrates the trade-off between the two commodities given his fixed budget. Any point on the line represents a combination of orange juice and yoghurt that Kante can afford. Points inside the triangle formed by the axes and the budget line are combinations he can afford, while points above the line are unaffordable. To visualize this, you would sketch a downward-sloping line starting from (0, 25) on the y-axis to (50, 0) on the x-axis.