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A school principal wants to buy some book cases for the school library. She can choose between two types of book case. Type A costs $10 and it requires 0.6 m2 of floor space and holds 1.2 m3 of books. The maximum floor space available is 7.2 m2 and the budget is $140 (but the school would prefer to spend less). What number and type of bookcases should the principal buy to get the largest possible storage space for books?

Respuesta :

MrRoyal

The principal should buy 8 of type A and 3 of type B to get the largest possible storage space for books

How to determine the number and type of book cases?

Let x represent type A and y represent type B,

So, we have the following table:

                            x            y        Available

Floor space       0.6         0.8            7.2

Budget               10          20             140

Book hold          0.8         1.2

Using the above table, we have the following linear model

Objective function Min Z = 0.8x + 1.2y

Subject to

0.6x + 0.8y ≤ 7.2

10x + 20y ≤ 140

x, y > 0

Using a graph, the solution to the above system of inequalities is:

(x,y) = (8,3)

Hence, the principal should buy 8 of type A and 3 of type B to get the largest possible storage space for books

Read more about objective functions at:

https://brainly.com/question/16826001

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