

InterviewSolution
Saved Bookmarks
1. |
A firm has to transport 1200 packages using large vans which can carry 200 packages each and small vans which can take 80 packages each. The cost for engaging each large van is 400 and each small van is 200. Not more than 3000 is to be spent on the job and the number of large vans cannot exceed the number of small vans. Formulate this problem, a LPP given that the objective is to minimise cost. |
Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :Let the firm has x number or large vans and y number of small vans. From the gives, information we have following corresponding constraint table. <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_NCERT_EXE_MATH_XII_C12_S01_012_S01.png" width="80%"/> <br/> Thus, we see that objective function for minimum cost is Z=400x+200y. <br/> Subject to constraints `200x+80y <a href="https://interviewquestions.tuteehub.com/tag/ge-1003146" style="font-weight:bold;" target="_blank" title="Click to know more about GE">GE</a> 2000["pakage constranit"]` <br/> `<a href="https://interviewquestions.tuteehub.com/tag/rightarrow-623803" style="font-weight:bold;" target="_blank" title="Click to know more about RIGHTARROW">RIGHTARROW</a> 5x+2y ge 30....(i)` <br/> and `400x+200y <a href="https://interviewquestions.tuteehub.com/tag/le-540308" style="font-weight:bold;" target="_blank" title="Click to know more about LE">LE</a> 3000["cost constraint"]`<br/> `Rightarrow 2x+y le 15 ...(ii)` <br/> and `x le y ..["van constraint"]...(iii)` <br/> and `x ge 0, y ge 0 ["non negative constraints"]...(iv)` <br/> Thus, <a href="https://interviewquestions.tuteehub.com/tag/required-1185621" style="font-weight:bold;" target="_blank" title="Click to know more about REQUIRED">REQUIRED</a> LPP to minimise cost is minimise `Z=400x+200y, "subject to " 5x+2y ge 30` <br/> `2x+y le 15` <br/> `x le y` <br/> `x ge 0, y ge 0`</body></html> | |