SPM 2023 Add Maths Paper 2, Question 14Linear Programming

Julie produces two types of dolls, Mal and Tod. Table 3 shows: Mal — x units at RM16.80 per unit; Tod — y units at RM14.00 per unit. The dolls satisfy the following constraints: I: the total number of Mal and Tod dolls is less than p units; II: the number of Tod dolls is more than q units; III: the number of Tod dolls is not more than 2 times the number of Mal dolls.

(a) Constraints I and II are shown on the provided graph; the shaded region represents the points satisfying both. State the value of p and of q.

Constraint III: the number of Tod dolls is not more than 2 times the number of Mal dolls; p = 16, q = 4.

(b) Write an inequality for constraint III, other than x ≥ 0 and y ≥ 0. Hence, construct and label the region R which satisfies all the constraints.

Use the region R constructed in (b).

(c)(i) On a particular day, the ratio of the number of Tod dolls to the number of Mal dolls produced is 3 : 2. Determine the possible numbers of Mal dolls produced on that day.

Mal costs RM16.80 per unit and Tod costs RM14.00 per unit; region R is as in (b).

(c)(ii) Given that the total cost to produce the Mal dolls and Tod dolls is RMk, express k in terms of x and y. Hence, draw the objective function and find the maximum cost.