Statistics for Management and Economics (Book Only)
11th Edition
ISBN: 9781337296946
Author: Gerald Keller
Publisher: Cengage Learning
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Chapter 5.3, Problem 15E
To determine
Stratified random sample:
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A company produces and sells a consumer product and thus far
has been able to control the volume of the product by varying
the selling price. The company is seeking to maximize its net
profit. It has been concluded that the relationship between price
and demand, per month, is approximately D = 500 - 5p, where p
is the price per unit in dollars. The fixed cost is $1,000 per
month, and the variable cost is $20 per unit. Obtain the answer
mathematically to the following questions:
a.What is the optimal number of units that should be produced and sold per month?
b. What is the maximum profit per month?
c.What are the breakeven sales quantities and the range of profitable demand volume?
A strawberry growing company is deciding its production and sale plan for the national and international markets.The sale price for each ton of strawberry depends on the quantity offered in the market. If x1 tons is offered for the domestic market, the sale price will be (30 - x1) CU / ton, while if x2 tons is offered for the international market, the sale price will be (40 - x2) CU / ton.The cost for each ton of strawberry for the domestic market is 10 MUs, while for the international market it is 15 MUs.The company has the capacity to produce up to 10 tons of strawberries for sale and, according to SAG restrictions, it must dedicate at least 10% of its production to the international market.For technical production reasons, the company must additionally satisfy the following restriction: x12 + x22 ≤64.a) Raise the NLP model that allows maximizing the net profit for the companyb) State the KKT conditions for the problem and indicate whether they are necessary and / or sufficient.c)…
A strawberry growing company is deciding its production and sale plan for the national and international markets.The sale price for each ton of strawberry depends on the quantity offered in the market. If x1 tons is offered for the domestic market, the sale price will be (30 - x1) CU / ton, while if x2 tons is offered for the international market, the sale price will be (40 - x2) CU / ton.The cost for each ton of strawberry for the domestic market is 10 MU, while for the international market it is 15 MU.The company has the capacity to produce up to 10 tons of strawberries for sale and according to SAG restrictions, it must dedicate at least 10% of production to the international market.For technical production reasons, the company must additionally satisfy the following restriction: x12 + x22 ≤64.d) There is the option of buying new machinery to increase the production capacity of the company. In what range should the new machine increase production capacity to suit the company? How…
Chapter 5 Solutions
Statistics for Management and Economics (Book Only)
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