SPM 2020 Add Maths Paper 2, Question 14Linear Programming

Diagram 8 shows two types of gift basket sold in a shop: a Premium basket (sold at RM80) and an Economy basket (sold at RM60). Table 2 gives the contents and cost: Premium has 8 apples, 2 oranges, 5 roses, cost RM45; Economy has 2 apples, 4 oranges, 5 roses, cost RM40. The shop owner buys fruits and flowers and repacks them into the two basket types. To minimise the cost for one week's sale, she must purchase at least 160 apples, the number of oranges must be more than 120, and the number of roses bought must be less than 250. Let x = number of Premium baskets and y = number of Economy baskets. (a) Using x for Premium and y for Economy baskets, write three inequalities, other than x >= 0 and y >= 0.

(b) Using a scale of 2 cm to 10 baskets on the x-axis and 2 cm to 5 baskets on the y-axis, construct and shade the region R which satisfies all the constraints.

(c) Using the graph constructed in 14(b), find the maximum profit earned by the shop owner every week. Hence, find the minimum number of apples that need to be purchased weekly.