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3 2 A tourist group wants to stay over for one day at the Eiland Spa Resort and must book their accommodation in advance. The

32 A tourist group wants to stay over for one day at the Eiland Spa Resort and must book
their accommodation in advance. The resort has a choice of two types of chalets
(cottages).
Type A: These chalets can host a couple and has a double bed.
Type B: These chalets can host a family and has a double bed and two single beds.
In the group there are at least 4 couples who want to stay in the type A chalets and
they want not less than 4 of the type B chalets to place families with four members.
The ratio of type A to type B must be at least one to two. The group needs 18 chalets
at the most.
Let the number of type A chalets be x and the number of type B be y.
3.2.1 Two of the constraints are x0 and y0.
Model the other constraints in respect of the above information in terms
of x and y.
3.2.2 The tariff fortype A is R1000/day and type B is R1500/day.
Write the equation that represents the total cost for the stay in terms of
x and y.
3.2.3 Determine the gradient or the search line. Show the steps.
3.2.4(a) Using a scale of 1 unit =2 chalets, represent the inequalities
graphically on the attached ADDENDUMB (5.2.4).
(b) Indicate the feasible region on the graph.
(c) Draw the search line on the graph and calculate the maximum cost
for theirstay.
3.2.5
Due to cancellations of tourists, the group on arrival consisted of 10
families who needed type B chalets and 3 couples who required type A
chalets.
Will the tour leader be able to meet the requirements of all the tourist in
their booked chalets? Give a reason for your answer with reference to the
feasible region.
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