Wormwood, Ltd., produces a variety of furniture products. The planning committee wants to prepare an aggregate plan for the next
six months using the following information: MONTH 1 2 3 4 5 6 Demand 160 150 160 180 170 140 Capacity Regular 150 150 150 150 160 160 Overtime 10 10 0 10 10 10 Cost Per Unit Regular time $ 50 Overtime 75 Subcontract 80 Inventory, per period 4 Subcontracting can handle a maximum of 10 units per month. Beginning inventory is zero. Develop a plan that minimizes total cost. No back orders are allowed. Regular production and overtime production can be less than capacity in any month.
1 answer:
Answer:
Wormwood limited
Production plan that will yield the least cost of $49,630 is shown in the attached document.
It entails maxing out the regular capacity from period 1 to 5, and using regular to produce only 140 units in period 6
It further entails using overtime to produce 10 units from period 1 to 5. And subcontracting only in period 4 to cover the demand/production gap.
This will keep inventory of 10 units in period 2, which is carried into period 3 and consumed in period 4.
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a. The point estimate of the married people that sleep well is = 0.6299. The confidence interval for the mean hours of sleep for those that have never been married but report good sleep is 0.6186, 0.6412
b. The point estimate of the number of hours for people that have never been married = 7.2257
95% confidence interval for the mean number of hours of sleep for those who have never been married = 7.2065, 7.2447
c. the estimated number of sleep for those that have never been married = 7.729 hours
a. The point estimate
Those who have never been married n = 7044
Xp = those who sleep for 7 hours at least
To get Xp, the <u>excel function </u>
Countif(range, criteria)
Countif(A:A, >=7)
This gives Xp = 4437
Point estimate =
= 0.6299
The point estimate of the married people that sleep well is = 0.6299
At 95% interval of confidence,
α = 1-0.95 = 0.05
α/2 = 0.05/2 = 0.025
Z0.025 = 1.96 ( Use the standard probability normal table)
Margin of Error
=
= 0.0113
The 95% confidence interval
= 0.6299 - 0.0113 , 0.6299 + 0.0113
= 0.6186, 0.6412
The confidence interval for the mean hours of sleep for those that have never been married is 0.6186, 0.6412
b. Sample mean
x = ∑x/n
x = number of sleep of the never been married
Mean is calculated using excel function
Average(range)
Average(a:a)
This gives the sample mean = 7.2257
The point estimate of the number of hours for people that have never been married = 7.2257
<u>Standard deviation</u> using excel =
Stdev(A:A) = 0.8211
= 0.0192
The<u> confidence interval</u> =
= 7.2257-0.0192, 7.2257+0.0192
= 7.2065, 7.2447
95% confidence interval for the mean number of hours of sleep for those who have never been married = 7.2065, 7.2447
c. From the available data, the mean number of sleep per day that is gotten from the 4437 people that are unmarried and sleep healthily for at least 7 hours = 34295.1
Mean = 34295.1/4437
= 7.729
the estimated number of sleep for those that have never been married = 7.729 hours
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