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wlad13 [49]
2 years ago
15

A RSS Clothing manufacturer makes two types of jogging pants, design A and design B. The design A jogging pants sells to the ret

ail stores for 2,500each and the design B jogging pants for 2,100. The cost for manufacturing each design A is 1,750 and the cost of each design B is 1,200. If the manufacturer makes no more than 120 jogging a week and budget no more than 150,000 per week, how many of each type should be made to maximize profit?

Mathematics
1 answer:
nikdorinn [45]2 years ago
8 0

Answer:

  120 of design B

Step-by-step explanation:

The profit per dollar cost for design A is (2500/1750 -1) ≈ 0.43. For design B, it is (2100/1200 -1) ≈ 0.75. Design B is more profitable and less expensive to make, so its production should be maximized.

For maximum profit, 120 jogging pants of design B should be made each week.

_____

The budget of 150,000 would allow 150,000/1,200 = 125 pants of design B to be made. The production limit of 120 pants does not use the entire budget.

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You can observe in the figure that:

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m\angle AVC+m\angle CVB=m\angle AVB\\\\39\°+23\°=62\°

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Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that  

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And the statistic is given by this formula:

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}

Where t follows a t distribution with n_1+n_2 -2 degrees of freedom and the pooled variance S^2_p is given by this formula:

S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}

The system of hypothesis on this case are:

Null hypothesis: \mu_1 = \mu_2

Alternative hypothesis: \mu_1 \neq \mu_2

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n_1 =20 represent the sample size for group 1

n_2 =20 represent the sample size for group 2

\bar X_1 =43.5 represent the sample mean for the group 1

\bar X_2 =40.1 represent the sample mean for the group 2

s_1=4.1 represent the sample standard deviation for group 1

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And the deviation would be just the square root of the variance:

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Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

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