A bakery sells a cake for Rs. 450 and a box of pastries for Rs. 90. It costs Rs. 330 to make a cake and Rs. 55 to make a box of pastries. If x cakes and y boxes of pastries are made and all are sold, the objective function for maximising the profit is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(Z = 120x + 35y\)
The profit on one item is its selling price minus its cost.
Profit on a cake \(= 450 - 330 = 120\)
Profit on a box of pastries \(= 90 - 55 = 35\)
For x cakes and y boxes, the total profit is
\(Z = 120x + 35y\)
Why the other options are incorrect
Option (1) \(Z = 450x + 90y\) — Incorrect. This is the sales income, not the profit.
Option (2) \(Z = 330x + 55y\) — Incorrect. This is the cost of making the items.
Option (3) \(Z = 35x + 120y\) — Incorrect. The profits are swapped: Rs. 120 is earned on a cake, which is x.