SOLUTION: A computer store sells two types of laptops, an all-purpose laptop and a gaming laptop. The supplier demands that at least 150 of these laptops be sold each month. Experience shows

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Question 1175827: A computer store sells two types of laptops, an all-purpose laptop and a gaming laptop. The supplier demands that at least 150 of these laptops be sold each month. Experience shows that most consumers prefer all-purpose laptops, but some younger consumers prefer gaming laptops. The result is that the number of all-purpose laptops sold is at least twice the number of gaming laptops sold. The store pays its sales staff a $43.27 commission for each all-purpose laptop sold and a $49.73 commission for each gaming laptop sold. How many of each type of laptop should be sold to minimize commission? What is that minimum monthly commission?
All-purpose laptops:
Gaming laptops:
Commission (dollars):
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = number of all purpose computers and y = number of gaming computers.

your objective function is commision = 43.27 * x + 49.73 * y

this is what you want to minimize.

your constraints are:

x + y >= 150
x >= 2 * y
x >= 0
y >= 0

using the desmos.com calculator, graph the opposite of the inequalities.

the unshaded area of the graph is the region of feasibility.

your minimum commission will be at the corner points of the feasible region.

the graph looks like this.



from the graph, it looks like there are 2 corner points.

at x = 100 and y = 50, the commission is equal to 6813.5
at x = 150 and y = 0, the commission is equal to 6390.5.

the least commission is paid when the number of general purpose laptops sold is 150 and the number of gaming laptops sold is 0.

you are evaluating the objective function at each of the corner points.
all the constraints need to be saisfied as well.
for example:
at x = 100 and y = 50, the objective function is 100 * 43.27 + 50 * 49.73 = 6813.5
the constraints of x >= 0 and y >= 0 are satisfied.
the constraints of x + y >= 150 are also satisfied.