The Cheery Cherry Chair Company makes three types of chairs, the Montegue, the Capulet, and the Verona. Each chair requires assembly, finishing, and a certain amount of wood to make. The assembly area can be used for at most 7 hours per day. To keep him busy, the finishing person needs to work at least 6 hours per day. Producing a Monteguerequires 1 hour of assembly, 2 hour of finishing, and 6 board feet of wood. Producing a Capulet requires 1 hour of assembly, 1 hour of finishing, and 6 board feet of wood. Finally, producing a Verona requires 2 hour of assembly, 1 hour of finishing, and 2 board feet of wood. If the company wants to minimize the amount of cherry wood used, how many should they make of each model? (It is possible to complete a fractional part a chair in a given day; in the long run you end up with completed chairs.) Number of Montegues =
Number of Capulets =
Number of Veronas =

How many board feet of cherry wood would be used each day?

x₁  =  1.6667       x₂  =  0      x₃   =  2.6667

z(minimum)  =  15.3333

Step-by-step explanation:

                                Assembly     Finishing      wood

Montegue  (x₁)               1                    2                 6

Capulet      (x₂)               1                    1                  6

Verona       (x₃)               2                    1                  2

Availability                

Assembly area  at most  7 hours

Finishing  area  at least  6 hours

Then

Objective Function  

z  =  6*x₁  +  6*x₂ + 2*x₃         to minimize

Subject to:

Constraint 1

Assembly area  at most  7 hours

x₁  +  x₂   +  2*x₃    ≤  7

Constraint 2

Finishing  area  at least  6 hours

2*x₁  +  x₂  +  x₃   ≥  6

General constraints     x₁  ≥ 0         x₂ ≥ 0           x₃ ≥0

Solution after 3 iterations with the help of on-line solver

x₁  =  1.6667       x₂  =  0      x₃   =  2.6667

z(minimum)  =  15.3333

$25

step-by-step explanation:

25 - 4.50 = 20.5

20.5 / 2 = 10.25

10.25 + 10 = 20.25

20.25 - 12.50 = 7.75

therefore the answer is $25 as shown as the first number.