Sentry wants to determine the least expensive way ofmanufacturing and shipping locks from its plants to thedistributors. Because the total demand from distributorsexceeds the total production capacity for all the plants,Sentry realizes it will not be able to satisfy all the demandfor its product, but wants to make sure each distributor willhave the opportunity to fill at least 80% of the ordersreceived.a. Create a spreadsheet model for this problem andsolve it.b. What is the optimal solution? The Sentry Lock Corporation manufactures a popularcommercial security lock at plants in Macon, Louisville,Detroit, and Phoenix. The per unit cost of production ateach plant is $35.50, $37.50, $39.00, and $36.25, respectively,while the annual production capacity at each plant is 18,000,15,000, 25,000, and 20,000, respectively.Sentry's locks are sold to retailers through wholesaledistributors in seven cities across the United States. The unitcost of shipping from each plant to each distributor issummarized in the following table along with the forecasteddemand from each distributor for the coming year.Unit Shipping Cost to Distributor inSt. LouisPlantsTacomaSan DiegoDallasDenverTampaBaltimoreMacon$2.50$2.75$1.75$2.00$2.10$1.80$1.65Louisville$1.50$1.85$1.90$2.25$1.85$1.90$1.60$1.00$1.85Detroit$2.30$2.25$1.25$1.50$2.00$1.908,500$1.7512,600Phoenix$0.90$2.50$2.65$1.6013,500$2.00Demand14,50018,00015,0009,000

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Description: Sentry wants to determine the least expensive way ofmanufacturing and shipping locks from its plants to thedistributors. Because the total demand from distributorsexceeds the total production capacity for all the plants,Sentry realizes it will not b

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a. Create a spreadsheet model for this problem and solve it. b. What is the optimal solution?

A First Course in Probability (10th Edition)

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Question

Sentry wants to determine the least expensive way of
manufacturing and shipping locks from its plants to the
distributors. Because the total demand from distributors
exceeds the total production capacity for all the plants,
Sentry realizes it will not be able to satisfy all the demand
for its product, but wants to make sure each distributor will
have the opportunity to fill at least 80% of the orders
received.
a. Create a spreadsheet model for this problem and
solve it.
b. What is the optimal solution?

The Sentry Lock Corporation manufactures a popular
commercial security lock at plants in Macon, Louisville,
Detroit, and Phoenix. The per unit cost of production at
each plant is $35.50, $37.50, $39.00, and $36.25, respectively,
while the annual production capacity at each plant is 18,000,
15,000, 25,000, and 20,000, respectively.
Sentry's locks are sold to retailers through wholesale
distributors in seven cities across the United States. The unit
cost of shipping from each plant to each distributor is
summarized in the following table along with the forecasted
demand from each distributor for the coming year.
Unit Shipping Cost to Distributor in
St. Louis
Plants
Tacoma
San Diego
Dallas
Denver
Tampa
Baltimore
Macon
$2.50
$2.75
$1.75
$2.00
$2.10
$1.80
$1.65
Louisville
$1.50
$1.85
$1.90
$2.25
$1.85
$1.90
$1.60
$1.00
$1.85
Detroit
$2.30
$2.25
$1.25
$1.50
$2.00
$1.90
8,500
$1.75
12,600
Phoenix
$0.90
$2.50
$2.65
$1.60
13,500
$2.00
Demand
14,500
18,000
15,000
9,000

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