helpQUESTION $2[20$ MARKS$]$

Toysr is a toy company that produces two types of toys which are toy cars and dolls. The

production of these toys requires two raw materials, wood and plastics. The toy car requires $2$

units of wood and $4$ units of plastics, whereas dolls require $5$ units of wood and $2$ units of

plastics. Toysr have $100$ units of wood and $100$ units of plastics in their inventory. Toysr obtains

RM$3$ for each unit of toy cars and RM$2$ for each unit of dolls.

$($a$)$ Suppose Toysr should produce the toys, such that the number of toys must be in

integers. Formulate the Toysr production planning as an integer programming model

with the objective to maximize the profit.

$[5$ Marks$]$

$[$C$01,$ P$01,$ C$3]$

$($b$)$ Solve the sub$-$optimal mix of the product graphically using the branch and bound

algorithm.