A bakery makes cakes. The bakery operates for 6 days each week. The matrix (mathbf M) shows the number of cakes of different types that are made each day.
(mathbf M) | Small | Medium | Large |
|---|
| Chocolate | \(8\) | \(5\) | \(2\) |
| Blackforest | \(6\) | \(4\) | \(3\) |
Evaluate the matrix (mathbf P=6mathbf M).[1]
Small cakes cost $10 to make. Medium cakes cost $15 to make. Large cakes cost $20 to make. Represent these amounts in a (3 imes1) matrix (mathbf N).[1]
Evaluate the matrix (mathbf T=mathbf{PN}).[2]
State what each of the elements of (mathbf T) represents.[1]
The bakery sells each cake for 70% more than it costs to make. One week they sold (dfrac23) of each size of the chocolate cakes and (dfrac56) of each size of the blackforest cakes made that week. The unsold cakes were given away. Calculate the total amount of profit the bakery made that week.[4]