Linear Programming
Madhya Pradesh Board · Class 12 · Mathematics
Flashcards for Linear Programming — Madhya Pradesh Board Class 12 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedफर्नीचर डीलर की समस्या का हल कीजिए: एक डीलर के पास निवेश करने के लिए 50,000 रुपये हैं, अधिकतम 60 फर्नीचर रखने की जगह है, टेबल पर 250 रुपये और कुर्सी पर 75 रुपये का लाभ है। कितनी टेबल और कुर्सियों पर अ
Answer
चरण 1: मान लीजिए x = tables, y = chairs. चरण 2: बाध्यताएँ लिखें: 2500x + 500y ≤ 50000, इसलिए 5x + y ≤ 100; x + y ≤ 60; x ≥ 0, y ≥ 0. चरण 3: उद्देश्य फलन: Z = 250x + 75y. चरण 4: व्यवहार्य क्षेत्र के को…
Solve the furniture dealer problem: A dealer has Rs 50,000 to invest, storage for at most 60 pieces, table profit Rs 250, chair profit Rs 75. How many tables and chairs give maximum profit?
Answer
Step 1: Let x = tables, y = chairs. Step 2: Write constraints: 2500x + 500y ≤ 50000, so 5x + y ≤ 100; x + y ≤ 60; x ≥ 0, y ≥ 0. Step 3: Objective function: Z = 250x + 75y. Step 4: Corner points of the…
Apply the investment constraint to the furniture dealer problem. Simplify 2500x + 500y ≤ 50000.
Answer
Step 1: Start with 2500x + 500y ≤ 50000. Step 2: Divide every term by 500. Step 3: 5x + y ≤ 100. Answer: The simplified investment constraint is 5x + y ≤ 100, where x = tables and y = chairs.
फर्नीचर डीलर की समस्या पर निवेश की बाध्यता लागू करें। 2500x + 500y ≤ 50000 को सरल कीजिए।
Answer
चरण 1: 2500x + 500y ≤ 50000 से शुरू करें। चरण 2: प्रत्येक पद को 500 से विभाजित करें। चरण 3: 5x + y ≤ 100। उत्तर: सरलीकृत निवेश बाध्यता 5x + y ≤ 100 है, जहाँ x = tables and y = chairs.
फर्नीचर की समस्या में यदि विक्रेता केवल मेज खरीदता है तो लाभ ज्ञात कीजिए।
Answer
चरण 1: केवल मेज़ें खरीदी जाती हैं, y = 0. चरण 2: 2500x ≤ 50000 से, x = 20 tables. चरण 3: प्रोफिt = 250 × 20 = Rs 5000. उत्तर: लाभ 5000 रुपये है।…
Find the profit if the dealer buys only tables in the furniture problem.
Answer
Step 1: If only tables are bought, y = 0. Step 2: From 2500x ≤ 50000, x = 20 tables. Step 3: Profit = 250 × 20 = Rs 5000. Answer: The profit is Rs 5000.
Find the profit if the dealer buys only chairs in the furniture problem.
Answer
Step 1: If only chairs are bought, x = 0. Step 2: 500y ≤ 50000 gives y = 100, but storage allows at most 60 pieces. Step 3: So y = 60 chairs. Step 4: Profit = 60 × 75 = Rs 4500. Answer: The profit is …
फर्नीचर की समस्या में यदि विक्रेता केवल कुर्सियाँ खरीदता है तो लाभ ज्ञात कीजिए।
Answer
चरण 1: यदि केवल कुर्सियाँ खरीदी जाती हैं, तो x = 0. चरण 2: 500y ≤ 50000 से y = 100 प्राप्त होता है, लेकिन भंडारण में अधिकतम 60 टुकड़े ही रखे जा सकते हैं। चरण 3: तो y = 60 chairs. चरण 4: प्रोफिt = 60 ×…
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