A furniture trader deals in only two items- chairs and tables. He has Rs. 50,000 to invest and a space to store atmost 35 items. A chair costs him Rs. 1000 and a table costs him Rs 2000. The trader earns a profit of Rs. 150 and Rs. 250 on a chair and a table, respectively. Choose the correct option among following that describes the given linear programming problem (LPP) to maximize the profit (where x and y are the number of chairs and tables that trader buys and sells)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Maximize $Z = 150x + 250y$, Subjected to constants, $x + y ≤35,x + 2y ≤ 50, x ≥0, y ≥0$
Let x = number of chairs, y = number of tables
Objective function (Profit to maximize):
$Z = 150x + 250y$
Constraints:
1. Investment constraint: 1000x + 2000y ≤ 50,000
2. Space constraint: x + y ≤ 35
3. Non-negativity constraints: x ≥ 0, y ≥ 0
Therefore, the LPP is:
Maximize Z = 150x + 250y
Subject to:
1000x + 2000y ≤ 50,000
x + y ≤ 35
x ≥ 0, y ≥ 0