S1 (Part x
1 answer:
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Answer:
Maximum Profit = 13050
when
The Toy company sells Jordan Size hoops = 7
The Toy company sells Shaq Size hoops = 3
Step-by-step explanation:
Given - The Toy Company sells two types of kids' basketball hoops, Jordan size and Shaq size. A neighborhood needs no more than 10 Jordan sizes and Shaq sizes all together. The Company requires the neighborhood to order at least 2 Jordan sizes and at least 3 Shaq sizes. The Toy Company makes a profit of $1,350 on the Jordan size and $1,200 on the Shaq size.
To find - What is the maximum profit they can make given the constraints above?
Proof -
Let us assume that,
The Toy company sells Jordan Size hoops = x
The Toy company sells Shaq Size hoops = y
Now,
Given that, A neighborhood needs no more than 10 Jordan sizes and Shaq sizes all together.
⇒x + y ≤ 10
Now,
Given that, The Company requires the neighborhood to order at least 2 Jordan sizes and at least 3 Shaq sizes.
⇒ x ≥ 2
y ≥ 3
Now,
Given that,
The Toy Company makes a profit of $1,350 on the Jordan size and $1,200 on the Shaq size.
So,
The objective function becomes
Z = 1350x + 1200 y
So,
The Linear Programming Problem (LPP) becomes
Maximize Z = 1350x + 1200 y
Subject to
x + y ≤ 10
x ≥ 2
y ≥ 3
x, y ≥ 0
We will Solve the LPP by Graphical method.
The graph is as follows :
The points on the Boundary are -
A(2, 8)
B(2, 3)
C(7, 3)
So,
Points (x,y) Objective function value ( Z = 1350x + 1200y)
B(2,3) 1350(2) + 1200(3) = 6300
C(7,3) 1350(7) + 1200(3) = 13050
A(2,8) 1350(2) + 1200(8) = 12300
So,
Maximum value = 13050 at point C(7,3)
∴ we get
Maximum Profit = 13050
when
The Toy company sells Jordan Size hoops = x = 7
The Toy company sells Shaq Size hoops = y = 3
Answer:
Step-by-step explanation:
Given that:
A study is conducted and the study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands.
a)
Thus; we formulate the null and the alternative hypotheses as follows:
The proportion is ; = 0.64
Null hypothesis:
The Null hypothesis states that there is no evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.
Alternative hypothesis:
The Alternative hypothesis states that there is evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.
b)
The proportion of the population = 0.64
The sample size n = 100
The number of shoppers = 52 stating that the supermarket brand was as good as the national brand
The sample proportion
The z - value is calculated by the formula:
z = -2.50
Since z = -2.50
the p-value = 2P(Z ≤ -2.50)
p-value = 2 × 0.0062
The p-value = 0.0124
c)
At significance level, ∝ = 0.05 ; The p-value = 0.0124
According to the rejection rule, if p-value is less than 0.05 then we will reject null hypothesis at ∝ = 0.05
Hence, the p-value =0.0124 < ∝ (=0.05)
According to the reject rule; reject null hypothesis.
Conclusion: There is no evidence at all that the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%.
d) we know that the significance level of ∝ = 0.05
The value is obtained as:
Now; to determine Z ; we locate the probability value of 0.05 form the table of standard normal distribution. Then we proceed to the left until the first column is reached and the value is 1.90. Also , we move upward until we reach the top and the value is 0.06. Now; the intersection of the row and column results the area to the left of z
This implies that :
The critical value for left tail is -1.96 and the critical value for right tail is 1.96.
Conclusion:
The critical value is -1.96 and the value of test statistic is - 2.50. Here, we can see that the value of test statistic is lesser than the critical value. Hence, we can be concluded that there is evidence that reject the null hypothesis.
Therefore, Yes, the national brand ketchup manufacturer is pleased with the conclusion.