‹ Back to the paper
Solve the following linear programming problem.
A manufacturing company produces two types of cell phones, Android and iOS. The company has…
A manufacturing company produces two types of cell phones, Android and iOS.
The company has resources to make at the most 300 sets a week. It takes ₹ 1800 to make an Android set and ₹ 2700 to make an iOS set. The company cannot spend more than ₹ 648000 a week to make cell phones. The company makes a profit of ₹ 510 per Android and ₹ 675 per iOS set. If $x$ and $y$ denote, respectively, the number of Android sets and iOS sets made each week, then formulate this problem as a Linear Programming Problem (LPP) given that the objective is to maximize the profit. Based on it, answer the questions that follow.
(a)[1.0]
What will be the maximum profit function on $x$ and $y$ sets? (write your objective based on the above data).
(b)[1.0]
What will be the values of your objective function in the feasible region? (at corner points)
(c)[1.0]
At what point the maximum profit will occur?
(d)[1.0]
What’s the weekly cost (in ₹) of manufacturing the sets?
Answer
Answer (a)
Official answer keyLet $x$ and $y$ denote, respectively, the number of Android and iOS cell phones. Thus, $x \geq 0$, $y \geq 0$. Since, the company can make at most 300 sets a week, therefore, $x + y \leq 300$.
Weekly cost (in ₹) of manufacturing the set is $1800x + 2700y$ and the company can spend up to ₹ 648000. Therefore, $1800x + 2700y \leq 648000$, i.e., $2x + 3y \leq 720$.
Objective function is Maximize $Z = 510x + 675y$.
Final answer: Maximize $Z = 510x + 675y$
Answer (b)
Official answer keyValues of objective function $Z = 510x + 675y$ at corner points: C(0, 240): 162000; B(180, 120): 172800; A(300, 0): 153000; O(0, 0): 0.
Final answer: C(0,240): 162000; B(180,120): 172800; A(300,0): 153000; O(0,0): 0
Answer (c)
Official answer keyMaximum $Z$ is 172800 at the point B(180, 120).
Answer (d)
Official answer keyWeekly cost $= 1800 \times 180 + 2700 \times 120 = 648000$.
From ISC 2025 Practice Mathematics, question 124.
Check your working with the LPP solver (graphical method): linear programming by the graphical method: the feasible region drawn, corner points and the optimum.