A vocational school enrols \(x\) girls for sewing class and \(y\) boys for carpentry class.

The fees per month for each girl and boy are \(\text{RM }800\) and \(\text{RM }300\) respectively.

The intake of the students is based on the following constraints.

i   : The total amount of fees collected per month is not less than \(\text{RM }2\, 400.\)

ii  : The number of boys exceed half the number of girls by \(4\) or less.

iii : The ratio of the number of boys to the number of girls is at least \(3:2.\)

Using a scale of \(2 \text { cm}\) to \(1\) student on both axes, construct and shade the region \(R\) which satisfies all the above constraints.

From your graph, find the range of the total number of students that the school can take.

\(5 \le c \le 10\)

In a fund raising activity, the Drama Club sells two types of ticket for a cultural show.

The club sells \(x\) tickets to members and \(y\) tickets to non-members.

The price of a ticket sold to members is \(\text{RM }20\) while the price of a ticket sold to non-members is \(\text{RM }30\).

The number of tickets sold depends on the following constraints.

i   : The number of tickets sold to non-members cannot exceed three times the number of tickets sold to members.

ii  : The hall can only accommodate a total of \(80\) people.

iii : The club needs to collect at least \(\text{RM }P\) for the show which is represented by the shaded region in the graph below.

Construct and shade the region \(R\) which satisfies all the above constraints.

From the graph constraints, find the range of tickets sold to non-members if the number of tickets sold to members is \(30\).

\(30 \le y \le 60\)

A confectionery bake two types of cakes, \(P\) and \(Q\) by using an oven.

In a day the oven produces \(x\) cakes \(P\) and \(y\) cakes \(Q\).

The time required to bake a cake \(P\) is \(10\) minutes and the time required to bake a cake \(Q\) is \(20\) minutes.

The baking of cake is based on the following constraints.

i   : The total number of cakes baked must be more than or equal to \(12\) units in a day.

ii  : The oven can operate for only \(5\) hours a day.

iii : The ratio of the number of cake \(P\) to cake \(Q\) is at most \(3:1.\)

Using a scale of \(2 \text{ cm}\) to \(5\) cakes on both axes, construct and shade the region \(R\) which satisfies all the above constraints.

Based on the graph constructed, find the range of profit that can be obtained if the selling price of a cake \(P\) is \(\text{RM }15\) and the selling price of a cake \(Q\) is \(\text{RM }12\).

\(\text{RM }144 \le \text{profit} \le \text{RM }342\)

A restaurant wants to buy two types of tables, \(M\) and \(N\), for its new outlet.

The price of a type \(M\) table is \(\text{RM }320\) and a type \(N\) table is \(\text{RM }240\).

The area of a tabletop of type \(M\) table and type \(N\) table are \(1 \text{ m}^2\) and \(2\text{ m}^2\) respectively.

The restaurant buys \(x\) tables of type \(M\) and \(y\) tables of type \(M\) and \(y\) tables of type \(N\).

The purchase of the table is based on the following constraints:

i   : The total area of all the tabletops is not less than \(60 \text{ m}^2\).

ii  : The total amount of money allocated is \(\text{RM } 19\,200\).

iii : The number of type \(N\) table is at most two times the number of type \(M\) table.

Using a scale of \(2 \text{ cm}\) to \(10\) tables on both axes, construct and shade the region \(R\) which satisfies all the above constraints.

Using the graph, find the range of the number of type \(M\) table if \(20\) type \(N\) tables are bought.

\(21 \le x \le 46\)

A restaurant wants to buy two types of tables, \(M\) and \(N\), for its new outlet.

The price of a type \(M\) table is \(\text{RM }320\) and a type \(N\) table is \(\text{RM }240\).

The area of a tabletop of type \(M\) table and type \(N\) table are \(1 \text{ m}^2\) and \(2\text{ m}^2\) respectively.

The restaurant buys \(x\) tables of type \(M\) and \(y\) tables of type \(M\) and \(y\) tables of type \(N\).

The purchase of the table is based on the following constraints:

i   : The total area of all the tabletops is not less than \(60 \text{ m}^2\).

ii  : The total amount of money allocated is \(\text{RM } 19\,200\).

iii : The number of type \(N\) table is at most two times the number of type \(M\) table.

Using a scale of \(2 \text{ cm}\) to \(10\) tables on both axes, construct and shade the region \(R\) which satisfies all the above constraints.

Using the graph, find the maximum number of customers that can use the tables at a time if a type \(M\) table can accommodate \(6\) customers and a type \(N\) table can accommodate \(12\) customers.

\(710\)