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Paisley and her children went into a restaurant where they sell hamburgers for $6.50 each and tacos for $4 each. Paisley has $80 to spend and must buy a minimum of 14 hamburgers and tacos altogether. If xx represents the number of hamburgers purchased and yy represents the number of tacos purchased, write and solve a system of inequalities graphically and determine one possible solution.

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samuelonum1

A possible solution to this problem is to buy 9.6 units of hamburgers and 4.4 units of Tacos

Linear Programming and Optimization

Given Data

  • Cost of one hamburgers = $6.50
  • Cost of one Tacos = $4
  • Total amount to spend = $80
  • Minimum number of Tacos and Hamburger to purchase = 14

Let x be the number of hamburgers purchased and y represents the number of tacos purchased

6.5x + 4y = 80-----1
x+y = 14 ------------2

Solve 1 and 2 simultaenously we have

multipl 1 by 1 and 2 by 5

6.5x + 4y = 80-----3

4x+4y=  56------------4

subtract 4 from 3 we have

2.5x  = 24

divide both sides by 2.5

x = 24/2.5

x = 9.6

Put x = 9.6 in 2 to find y

9.6+y = 14

y = 14-9.6

y = 4.4

Learn more about linear programming here:

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