A small private company sell two kinds of decorations, Type A and Type B for kids parties

Question

1. A small private company sell two kinds of decorations, Type A and Type B for kids parties. Each type A decoration needs 2units of labor and cost $0.8 to manufacture. Each type B decoration needs 5 units of labor and cost $2.50 to manufacture. The company has 3100 units of labor available for the decoration and set aside $1390  to be spent on decoration. given that the profit on each  type A decoration is $1.00 and the profit for each type B decoration is $3.06, how many of each decoration type should the company produce to maximize the profit? Find the maximum profit.

Answer 1

 

Hi Vivian,

 

Letting x and y represent the number of type A and type B to produce, respectively,

it's equivalent to maximize

 

     x + 3.06y                         (Eq. 1)

 

under the set of conditions

 

     x ≥ 0,                              (Eq. 2)

 

     y ≥ 0,                              (Eq. 3)

 

     2x + 5y ≤ 3100,               (Eq. 4)

 

     0.8x + 2.5y ≤ 1390           (Eq. 5)

 

Solving the system of inequalities, Eq. 2 anthrough Eq. 5,

we come up with four vertical points to be tested

to see which one results in the maximun of Eq. 1.

Out of those 4 vertices,

(x, y) = (800, 300) results in the maximum of Eq. 1.

 

The maximum profit will be $1718

if the company produce 800 type A and 300 type B decorations.