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. What is the maximum profit they can make given the constraints
above? (You can use Desmos to graph if you do not have any graph paper).
Lo

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

x=4

step-by-step explanation:

0.02

step-by-step explanation:

time of 9 192 631 770 periods of the radiation corresponding to the transition between the 2 hyperfine levels of the ground state of the caesium 133 atom at 0 k (but other seconds are sometimes used in astronomy)