A department has five employees with five jobs to be performed. The time (in hours) each employee will take to perform each job is given in the following matrix. How should the jobs be allocated, one per employee, so as to minimize the total man hours?
This problem is an assignment problem, which can be solved using the Hungarian algorithm to minimize the total man-hours. The given cost matrix is: \[ \begin{array}{c|ccccc} ________ _____ ________ ____ ________ __________ __________.
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Two breakfast food manufacturers ABC and XYZ are competing for an increased market share. The pay-off matrix, shown in the following table, describes the increase in market share for ABC and decrease in market share of XYZ. Determine optimal strategies for both the manufacturers and the value of the game.
निम्नलिखित खेल का ग्राफीय विधि से हल कीजिए:
नाश्ता बनाने वाली दो कम्पनियाँ ABC और XYZ बाजार में अपने शेयर बढ़ाने के लिए मुकाबला कर रही हैं। निम्नलिखित सारणी में दी गई भुगतान आव्यूह में ABC के बढ़ते बाजार शेयर और XYZ. के घटते बाजार शेयर दर्शाए गए हैं। दोनों कम्पनियों के लिए इष्टतम युक्तियाँ ज्ञात कीजिए और खेल का मान भी ज्ञात कीजिए।
Find the initial basic feasible solution of the following transportation problem using North-West Corner method.
| 90 | 90 | 100 | 110 | 200 |
| 50 | 70 | 130 | 85 | 50 |
| 75 | 100 | 100 | 30 |
एक विभाग में 5 जॉब करने के लिए 5 कर्मचारी हैं। प्रत्येक कर्मचारी द्वारा प्रत्येक जॉब को करने में लगने वाला समय (घंटों में) निम्नलिखित आव्यूह में दिया गया है। कुल श्रम शक्ति को न्यूनतम करने के लिए एक जॉब एक कर्मचारी को किस प्रकार आबंटित करना चाहिए?
A company makes two kinds of leather belts. Belts A is high quality belt and belt B is of lower quality. The respective profits on Aand B are ₹ 4 and ₹ 3 per belt. The production of each type Arequires twice as much time as a belt. The production of each type of type B, and if all belts were of type B, the company could make 1000 belts per day. The supply of leather is sufficient for only 800 belts per day (both A and B combined). Belt Arequire a fancy buckle and only 400 buckles per day are available. There are only 700 buckles a day available for belt B. What should be the daily production of each type of belt? Formulate this problem as an LP model and solve it by the graphical method.
Solve the following LPP graphically:
Maximize:
z= 10x1 + 10x2
subject to the constraints:
4x1 + 3x2 ≤ 12
6x1 +18x2 ≤ 36
X1,X2 ≥ 0.