A computer store sells two models. The first is a laptop which costs $950 to pro

Question

A computer store sells two models. The first is a laptop which costs $950 to produce, and a netbook which costs $500 to produce. It is estimated that the average selling price of the laptop is $1200 minus $0.5 for each netbook sold and minus $0.03 for each laptop sold. Similar esimates predict the average selling price of the netbook is $800 minus $0.2 for each laptop sold and minus $0.04 for each netbook sold. Suppose the store is limited to not more than 500 laptops, not more than 400 netbooks, and not more than 800 total. Compute the shadow price with respect to the production constraint of 800.

Use Maple

Explanation / Answer

x be number of laptops and y notebooks

constraints

x<=500

y<=400

x+y<=800

objective to be maximised

z=1200x-0.5xy-0.03x^2-950x+800y-0.2xy-0.04y^2-500y =250x-0.03x^2+300y-0.04y^2-0.7xy

optimal solution at 0,400

z=113600 $

if there is no 800 constraint

optimal sol at 0,400

z=113600$

there is no change in optimal solution...so there is no shadow price

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