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5 marksLinear Programming

CSEC Mathematics · 2022 · Paper 2 · Question 8(c)

On the grid below, plot the four lines associated with the inequalities in (a) and (b). Shade and label the region that satisfies ALL four inequalities R.

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  1. 8(a)Write down THREE inequalities, in terms of x and/or y, other than x \ge 0 and y \ge 0, to represent this information.[3 marks]
  2. 8(b)A car can carry 4 people and a minivan can carry 6 people. There are at most 60 persons to be taken on a tour. Show that 2x + 3y \le 30.[1 mark]
  3. 8(d)(i)Determine the two combinations for the MINIMUM number of cars and minivans that can be used to carry EXACTLY 60 people on the tour.[2 marks]
  4. 8(d)(ii)The company charges 75 to rent a car and 90 to rent a minivan. Show that the MINIMUM rental cost for this tour is $990.[1 mark]

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