A manufacturer produces two types of bottled coffee drinks: cappuccinos and cafés au lait. Each bottle of cappuccino requires 6
ounces of coffee and 2 ounces of milk and earns a profit of $0.40. Each bottle of café au lait requires 4 ounces of coffee and 4 ounces of milk and earns a profit of $0.50. The manufacturer has 720 ounces of coffee and 400 ounces of milk available for production each day. To meet demand, the manufacturer must produce at least 80 coffee drinks each day. Let x = the number of cappuccino bottles and y = the number of café au lait bottles. Complete the objective function.
The <em>objective function</em> is the function that you want to optimize: usually minimize in the case of costs, and maximize in the case of revenues or profits.
In this case, you know the <em>profits</em> that a manufacturer earns from two types of <em>bottled coffe drinks</em>: <em>cappuccinos</em> and <em>cafés au lait</em>.
Each bottle of <em>cappuccino earns a profit of $0.40</em> and each bottle of <em>café au lait earns a profit of $0.50</em>.
Then:
using the variable x for the number bottles of cappuccino produced, the profit earned from x bottles is 0.40x, and
using the variable y for the number of bottles of café au lait the produced, the profit earned from y bottles is 0.5y.
The total profit earned, P, is the sum of the profits earned from each type of bottled coffee drinks:
P = 0.40x + 0.50y
That is the <em>objective function</em>, i.e. the function that the manufacturer must try to maximize subject to the corresponding constraints.
