SOLUTION: Egypt Co. offers to the market two types of gadgets. Regarding the nature of the
production process, and there are not more than 60 hours of the whole operation process. A gadget
Algebra.Com
Question 1205691: Egypt Co. offers to the market two types of gadgets. Regarding the nature of the
production process, and there are not more than 60 hours of the whole operation process. A gadget of the regular type requires 1 hour of completing, while a premium gadget needs 3 hours of finishing. To keep the production alive, Egypt Co. must make at least 10 gadgets a day. The contribution of $3 is realized for each regular gadget and $9 for a premium gadget. The historical record suggests that the demand of premium gadget is increasing and is at least the demand of regular ones.
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52909) (Show Source): You can put this solution on YOUR website!
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Egypt Co. offers to the market two types of gadgets. Regarding the nature of the production process,
and there are not more than 60 hours of the whole operation process. A gadget of the regular type
requires 1 hour of completing, while a premium gadget needs 3 hours of finishing. To keep the production alive,
Egypt Co. must make at least 10 gadgets a day. The contribution of $3 is realized for each
regular gadget and $9 for a premium gadget. The historical record suggests that the demand
of premium gadget is increasing and is at least the demand of regular ones.
~~~~~~~~~~~~~~~~~~~~~
The post is incomplete.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = the number of regular gadgets.
y = the number of premium gadgets.
you get 3 dollars for every regular gadget and 9 dollars for every premium gadgets.
your constraint inequalities are:
x + y >= 10
x + 3y <= 60
y >= x
x >= 0
y >= 0
your objective function is:
3x + 9y which you want to maximize.
using the desmod.com calculator at https://www.desmos.com/calculator, you would:
graph the opposite of the inequalities.
the area on the graph that is not shaded is your region of feasibility.
you evaluate the objective function at each corner point of that region to find the corner point with the maximum contribution.
it appears that the coordinate points of (0,20) and (15,15) both contain the maximum contribution at 180 dollars each.
you would then decide which one of those you want to do based on other considerations, such as maybe you don't want to just make premium gadgets since there's a market for the regular gadgets as well.
here's what the graph looks like.
all the constraint inequalities are asatisfied at each corner point, as they should be.
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