a firm has to transport 1200 packages using large van which can carry 200 packages each and small van which - Maths - Linear Programming

Question

a firm has to transport 1200 packages using large van which can
carry 200 packages each and small van which can carry 80 packages
each The cost for engaging each large van is Rs 400 and each small
van is Rs 200 Not more than Rs 3000 is to be spent on the job and
number of large van cannot exceed the number of small van Formulate
the problem in LPP given that objective is to minimize cost

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

Let us first summarized the given data:For the large van:Packages=200 Cost=₹ 400For the small vanPackages=80Cost=₹200For the minimum requirementPackages=1200Cost=₹3000Let x be no of large vans and y be the number of small vans,used for carrying the packages
The objective is to minimize the cost
 The mathematic formulation of the above problem is as follows:200x+80y≥1200  Minimum PackagesDivide each term by 40⇒5x+2y≥30400x+200y≤3000 Maximum budget is 3000Divide each term by 200⇒2x+y≥15Number of large vans cannot exceed the number of small vans:⇒x≤yx≥0 and y≥0 Non-negativity constraint :
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