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Mr Wade imports and sells carbon road bikes and carbon mountain bikes. He sells at least 6 road bikes per week
and the ratio of road bikes to mountain bikes is at less than 5:2

The company manufacturing these bikes for Mr Wade has advised that each road bike takes 2.5 hours to make
and each mountain bike takes 4 hours to make. Under contract Mr Wade has hired the company's service for a
maximum of 40 hours a week. The profit on a road bike sale is $237 while on a mountain bike is $285.
Being a maths teacher, Mr Wade knows that linear programming is the best way to determine how many of each
bike to import sell to maximise profits.

a) Define your variables and list the system of inequalities for this question

Answer :

Edufirst

Answer:

c)  Conclusion:

The system of inequalities is:

  • 2.5r + 4m ≤ 40
  • r ≥ 0
  • m ≥ 0

Explanation:

1. Define the variables

  • r = number of carbon road bikes
  • m = number of carbon mountain bikes

2. List the system of inequalities

a) Time: maximum 40 hours a week

   i) From "each road bike takes 2.5 hours to make":

  • time to make r carbon road bikes: 2.5r

   ii) From "each mountain bike takes 4 hours to make""

  • time to make m carbon mountain bikes: 4m

   iii) Constraint:

  • time ≤ 40
  • 2.5r + 4m ≤ 40

b) Natural constraints:

Neither r nor m can be negative:

  • r ≥ 0
  • m ≥ 0

c)  Conclusion:

The system of inequalities is:

  • 2.5r + 4m ≤ 40
  • r ≥ 0
  • m ≥ 0

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