6 Kai mixes hot drinks using coffee and steamed milk.
The amounts ( ml ) needed and profit ( \(\pounds\) ) for a standard sized cup of four different drinks are given in the table. The table also shows the amount of the ingredients available.
| Type of drink | Coffee | Foamed milk | Profit |
| w Americano | 80 | 0 | 1.20 |
| \(x\) Cappuccino | 60 | 120 | X |
| \(y\) Flat White | 60 | 100 | 1.40 |
| \(z\) Latte | 40 | 120 | 1.50 |
| Available | 900 | 1500 | |
Kai makes the equivalent of \(w\) standard sized americanos, \(x\) standard sized cappuccinos, \(y\) standard sized flat whites and \(z\) standard sized lattes. He can make different sized drinks so \(w , x , y , z\) need not be integers.
Kai wants to find the maximum profit that he can make, assuming that the customers want to buy the drinks he has made.
- What is the minimum value of X for it to be worthwhile for Kai to make cappuccinos?
Kai makes no cappuccinos.
- Use the simplex algorithm to solve Kai's problem.
The grids in the Printed Answer Booklet should have at least enough rows and columns and there should be at least enough grids to show all the iterations needed.
Only record the output from each iteration, not any intermediate stages.
Interpret the solution and state the maximum profit that Kai can make.