Answer:
- <u><em>P = 0.40x + 0.50y</em></u>
Explanation:
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:
That is the <em>objective function</em>, i.e. the function that the manufacturer must try to maximize subject to the corresponding constraints.
Answer:
(-4, -8)
Step-by-step explanation:
Use the substitution method. x = -4, so y = (1/2)x - 6 becomes:
y = (1/2)(-4) - 6, or y = -2 - 6, or y = -8.
The solution is (-4, -8).
Let the three items be M, Y and P.
n{M ∩ Y} only = 4-3 = 1
n{M ∩ P) only = 5-3 = 2
n{ Y ∩ P} only = 2
n{M} only = 12-(1+3+2) = 6
n{Y} only = 10-(1+2+3) = 4
n{P} only = 14-(2+3+2) = 7
n{M∩P∩Y} = 3
Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.
Answer:
x = 50
Step-by-step explanation:
-3(52)=-3(x)+-3(2)
Divide both sides by -3
52 = x + 2
x = 50
(sqrt2 - sqrt6)/4 = - 0.259
cos ((7pi)/12) = cos 105 = - 0.259
