A small workshop can manufacture up to 120 units altogether of three products P, Q…
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
A small workshop can manufacture up to 120 units altogether of three products P, Q and R in one day. Because of a short-term marketing decision, the manager intends to offer only two of these three products for sale today.
The daily data are:
• Product P: requires 3 labour hours per unit, 2 machine hours per unit, profit Rs 80 per unit.
• Product Q: requires 5 labour hours per unit, 1 machine hour per unit, profit Rs 70 per unit.
• Product R: requires 2 labour hours per unit, 4 machine hours per unit, profit Rs 90 per unit.
Total labour available: 300 hours per day.
Total machine capacity: 240 hours per day.
Respond to the tasks below.
(i) Select any TWO of the three products to be produced today so that a two-variable model can be constructed. State a valid mathematical reason for your choice with reference to the profit coefficients.
(ii) Using your choice in part (i), formulate the complete two-variable optimisation problem, clearly stating the decision variables, the objective expression and ALL constraint inequalities including the non-negativity conditions.