Answer:
1. Objective function is a maximum at (16,0), Z = 4x+4y = 4(16) + 4(0) = 64
2. Objective function is at a maximum at (5,3), Z=3x+2y=3(5)+2(3)=21
Step-by-step explanation:
1. Maximize: P = 4x +4y
Subject to: 2x + y ≤ 20
x + 2y ≤ 16
x, y ≥ 0
Plot the constraints and the objective function Z, or P=4x+4y)
Push the objective function to the limit permitted by the feasible region to find the maximum.
Answer: Objective function is a maximum at (16,0),
Z = 4x+4y = 4(16) + 4(0) = 64
2. Maximize P = 3x + 2y
Subject to x + y ≤ 8
2x + y ≤ 13
x ≥ 0, y ≥ 0
Plot the constraints and the objective function Z, or P=3x+2y.
Push the objective function to the limit in the increase + direction permitted by the feasible region to find the maximum intersection.
Answer: Objective function is at a maximum at (5,3),
Z = 3x+2y = 3(5)+2(3) = 21
To solve this problem, we must recall that the formula
for velocity assuming linear motion:
v = d / t
Where,
v = velocity
d = distance
t = time
For condition 1: bus travelling on a level road
v1 = d1 / t1
<span>(v2 + 20) = (449 – d2) / 4 --->1</span>
For condition 2: bus travelling on a winding road
v2 = d2 / t2
<span>v2 = d2 / 5 --->2</span>
Combining equations 1 and 2:
(d2 / 5) + 20 = (449 – d2) / 4
0.8 d2 + 80 = 449 – d2
1.8 d2 = 369
d2 = 205 miles
Using equation 2, find for v2:
v2 = 205 / 5
v2 = 41 mph
Since v1 = v2 + 20
v1 = 41 + 20
v1 = 61 mph
Therefore
<span>the
average speed on the level road is 61 mph.</span>
-10 + a = 6a - 7a
Rearrange the left hand side
a - 10 = 6a - 7a
Simplify 6a - 7a
a - 10 = -a
Add a on both sides
2a - 10 = 0
Add 10 on both sides
2a = 10
Divide by 2 on both sides
a = 5
A. 11:30 P.M.
Hope this helps !!!!
Answer:
a) the probability is P(G∩C) =0.0035 (0.35%)
b) the probability is P(C) =0.008 (0.8%)
c) the probability is P(G/C) = 0.4375 (43.75%)
Step-by-step explanation:
defining the event G= the customer is a good risk , C= the customer fills a claim then using the theorem of Bayes for conditional probability
a) P(G∩C) = P(G)*P(C/G)
where
P(G∩C) = probability that the customer is a good risk and has filed a claim
P(C/G) = probability to fill a claim given that the customer is a good risk
replacing values
P(G∩C) = P(G)*P(C/G) = 0.70 * 0.005 = 0.0035 (0.35%)
b) for P(C)
P(C) = probability that the customer is a good risk * probability to fill a claim given that the customer is a good risk + probability that the customer is a medium risk * probability to fill a claim given that the customer is a medium risk +probability that the customer is a low risk * probability to fill a claim given that the customer is a low risk = 0.70 * 0.005 + 0.2* 0.01 + 0.1 * 0.025
= 0.008 (0.8%)
therefore
P(C) =0.008 (0.8%)
c) using the theorem of Bayes:
P(G/C) = P(G∩C) / P(C)
P(C/G) = probability that the customer is a good risk given that the customer has filled a claim
replacing values
P(G/C) = P(G∩C) / P(C) = 0.0035 /0.008 = 0.4375 (43.75%)
