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.

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Amiya Wolf · Accepted Answer

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&amp;gt;=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&amp;gt;=300  Also,  x&amp;gt;=0 and y&amp;gt;=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&amp;gt;=25 and 15x+10y&amp;gt;=300  Non-negative constraint x&amp;gt;=0, y&amp;gt;=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

Roger sells fire trucks and dolls to a toy store. He sells each fire truck for $15 and each doll for

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