SOLUTION: A store sells two models of laptop computers. Because of the demand, the store stocks at least three times as many units of model A as units of model B. The costs to the store for

Question 1120021: A store sells two models of laptop computers. Because of the demand, the store stocks at least three times as many units of model A as units of model B. The costs to the store for the two models are $700 and $1100, respectively. The management does not want more than $38,500 in computer inventory at any one time, and it wants at least fifteen model A laptop computers and five model B laptop computers in inventory at all times.
Find the system of inequalities describing all possible inventory levels. (Use x for units of product A and y for units of product B.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x equal the number of model A.
y equal the number of model B.

store stocks at least 3 times as many model A as B.

x >= 3y

costs are 700 for model A and 1100 for model B.

cost is less than or equal to 38500.

700x + 1100y <= 38500

store wants at least 15 model A and 5 model in B in store at all times.

x >= 15
y >= 5

your system of inequalities is:

x >= 3y
700x + 1100y <= 38500
x >=15
y >= 5

this system of inequalities leads to the following possible values for x and y, under the constraint that x and y have to be integers.

any points within the area of the graph that is not shaded are feasible.

this graph was created by graphing the opposite of the inequalities.

that shaded the region that was not feasible, leaving the region that was feasible not shaded.

the maximum / minimum value of your objective function are where the maximum and minimum values lie.

you would evaluate the objective function at these points.

for example, if the objective function was to minimize cost, then the point (15,5) would be the solution.

the objective function would be 700x + 1100y, in that case.

an example of any point in the feasible region would be the point (30,8).

that point meets all the constraints.

30 >= 3 * 8
30 >=15
8 >= 5
700*30 + 1100*8 = =29800 <= 38500

here's the graph.

$$$

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