Question

The Toy Company sells two types of kids' basketball hoops, Jordan size and Shaq size.

Answer 1

Answer:

Maximum Profit = 13050

when

The Toy company sells Jordan Size hoops = 7

The Toy company sells Shaq Size hoops = 3

Step-by-step explanation:

Given - The Toy Company sells two types of kids' basketball hoops, Jordan size and Shaq size.  A neighborhood needs no more than 10 Jordan sizes and Shaq sizes all together. The  Company requires the neighborhood to order at least 2 Jordan sizes and at least 3  Shaq sizes. The Toy Company makes a profit of $1,350 on the Jordan size and $1,200  on the Shaq size.

To find - What is the maximum profit they can make given the constraints  above?

Proof -

Let us assume that,

The Toy company sells Jordan Size hoops = x

The Toy company sells Shaq Size hoops = y

Now,

Given that,  A neighborhood needs no more than 10 Jordan sizes and Shaq sizes all together.

⇒x + y ≤ 10

Now,

Given that,  The  Company requires the neighborhood to order at least 2 Jordan sizes and at least 3  Shaq sizes.

⇒ x ≥ 2

   y ≥ 3

Now,

Given that,

The Toy Company makes a profit of $1,350 on the Jordan size and $1,200  on the Shaq size.

So,

The objective function becomes

Z = 1350x + 1200 y

So,

The Linear Programming Problem (LPP) becomes

Maximize Z = 1350x + 1200 y

Subject to

x + y ≤ 10

x ≥ 2

y ≥ 3

x, y ≥ 0

We will Solve the LPP by Graphical method.

The graph is as follows :

The points on the Boundary are -

A(2, 8)

B(2, 3)

C(7, 3)

So,

Points (x,y) Objective function value  ( Z = 1350x + 1200y)

B(2,3)            1350(2) + 1200(3) = 6300

C(7,3)           1350(7) + 1200(3) = 13050

A(2,8)                 1350(2) + 1200(8) = 12300

So,

Maximum value = 13050 at point C(7,3)

∴ we get

Maximum Profit = 13050

when

The Toy company sells Jordan Size hoops = x = 7

The Toy company sells Shaq Size hoops = y = 3