Question

Roger sells fire trucks and dolls to a toy store. He sells each fire truck for $15 and each doll for $10. Roger wants to sell at least 25 toys and needs to earn at least $300 to cover his costs. If each fire truck takes 50 minutes to make and each doll takes 45 minutes to make, how many fire trucks and dolls should Roger make to minimize the time spent making the toys.

Answer 1

Answer:

Number of Fire trucks made= 10.

Number of Dolls made =   15  

Step-by-step explanation:

Let x denote the number of fire trucks made.

and y denote the number of dolls made.

Now we are given:

• Roger wants to sell at least 25 toys .

Hence, the inequality that can be made  from this information is:

                       $x+y\geq 25$

• Also,

He sells each fire truck for $15 and each doll for $10.

He needs to earn at least $300 to cover his costs.

The inequality that can be made from this piece of information is:

                 $15x+10y\geq 300$

           Also,

                      x≥0

                 and y≥0

Each fire truck takes 50 minutes to make and each doll takes 45 minutes to make.

Now we are asked to minimize the time function let it denote by 'z'.

Hence, the system that is formed is:

Optimization function       Min.   z=50x+45y

    subject to                     x+y ≥ 25[/tex]

                                and   15x+10y ≥ 300[/tex]

Non-negative constraint         x ≥ 0

                                                 y ≥ 0

Now on solving the constraints we get the boundary points as:

(25,0) , (0,30) and (10,15)

Hence, the optimal solution is checked at these points.

(25,0)             z=1250

(0,30)            z=1350

(10,15)             z=1175

Hence, the minimal time spent is: 1175 minutes.

Number of Fire trucks made= 10.

Number of Dolls made =15  

Answer 2

Answer:

this is the correct answer for plato (Roger should make 10 fire trucks and 15 dolls in order to minimize the time spent making toys.)

Step-by-step explanation: