Answer Happy

PART 3 [15 marks]
A toy factory manufactures two types of wooden toys: soldiers and
trains. A soldier sells
for R27 and uses R10 worth of raw material and R14 worth labour. A
train sells for R21
and uses R9 worth of raw material and R10 worth of labour. The
manufacture of each toy
requires two types of labour: carpentry and finishing. A soldier
requires two hours of
finishing labour and one hour of carpentry labour. A train requires
one hour of finishing
labour and one hour of carpentry labour. Each week only 100 hours
of finishing labour
and 80 hours of carpentry labour are available. All the trains can
be sold, but at most 40
soldiers can be sold each week. Answer the following questions to
ultimately determine
how many soldiers and trains should be produced each week to
maximize profit if R520 is
budgeted for raw material and R650 is budgeted for labour
costs.
1. State the objective function and clearly
indicate if it is a maximization or a
minimization problem. (1)
2. State all the constraints. (3)
3. Clearly sketch a graph that show all
constraints and shade the solution space if it
exists. Also clearly label everything on the diagram including the
axes. (7)
4. Sketch the isoprofit(isocost) line on the
diagram in question 3 when the factory
makes R600 rand of profit. Then sketch the
isoprofit(isocost) line on the diagram in
question 3 when the factory makes the most money from having
optimally
produced and sold toy trains and toy soldiers. (2)
5. What is the optimal profit that the factory
makes? (1)
6. How many soldiers and trains leads to the
result in question 5. (1)