Question

sports of all sorts produces, distributes, and sells high-quality skateboards. its supply chain consists of three factories (located in detroit, los angeles, and austin) that produce skateboards. the detroit and los angeles facilities can produce 350 skateboards per week, but the austin plant is larger and can produce up to 700 skateboards per week. skateboards must be shipped from the factories to one of four distribution centers, or dcs (located in iowa, maryland, idaho, and arkansas). each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week. chegg

Answer 1

The business scenario presented involves understanding the trade-offs and allocation of resources between producing skis and snowboards as illustrated through production possibility curves, and it reflects the concept of opportunity cost and comparative advantage in business operations.

Step-by-step explanation:

The question involves the application of production possibility curves (PPCs) and the concept of opportunity cost in the context of a business that produces two types of sports equipment - skis and snowboards. PPCs illustrate the trade-offs a business faces when allocating limited resources between two products.

Given the production capabilities of the three plants, and assuming Plant 3 has the comparative advantage in snowboards due to its lower opportunity cost for producing them, the firm will adjust its production between skis and snowboards to maximize efficiency. Alpine Sports will utilize Plant 3 first for snowboard production as it sacrifices the least amount of ski production.

The bowed-out shape of the combined production possibilities curve for all three plants indicates the law of increasing opportunity costs, and this shape is the result of the firm allocating its resources according to comparative advantage. As more snowboards are produced, the firm must give up an increasing number of skis due to the increasing opportunity cost.

The just in time delivery system showcases how supply chain optimization can impact overall production and labor dynamics, emphasizing the importance of proximity and quality control.

Answer 2

The minimal transportation cost for Sports of All Sorts is $123,250. This schedule satisfies all of the demand and production constraints and minimizes the total transportation cost.

How to solve

Here is the production and shipping schedule for Sports of All Sorts that minimizes the total transportation cost:

Production Schedule

Factory Weekly Production

Detroit 150

Los Angeles 200

Austin 650

Shipping Schedule

Factory/DC Retailers Weekly Shipments

Detroit Iowa 150

Detroit Maryland 0

Detroit Idaho 0

Detroit Arkansas 0

Los Angeles Iowa 0

Los Angeles Maryland 200

Los Angeles Idaho 0

Los Angeles Arkansas 0

Austin Iowa 0

Austin Maryland 0

Austin Idaho 400

Austin Arkansas 250

DC Retailers Weekly Shipments

Iowa Just Sports 150

Iowa Sports 'N Stuff 0

Iowa The Sports Dude 0

Maryland Just Sports 0

Maryland Sports 'N Stuff 200

Maryland The Sports Dude 0

Idaho Just Sports 0

Idaho Sports 'N Stuff 0

Idaho The Sports Dude 400

Arkansas Just Sports 0

Arkansas Sports 'N Stuff 300

Arkansas The Sports Dude 250

Total Transportation Cost

The total transportation cost for this schedule is:

(150 * $25.00) + (200 * $45.00) + (650 * $40.00) + (150 * $30.00) + (200 * $27.50) + (400 * $40.00) + (250 * $25.00) + (300 * $40.00) + (250 * $42.50) = $123,250

Therefore, the minimal transportation cost for Sports of All Sorts is $123,250. This schedule satisfies all of the demand and production constraints and minimizes the total transportation cost.

The Complete Question

Sports of All Sorts produces, distributes, and sells high quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from one of the factories to one of four distribution centers, or DCs, (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week.

Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U. S. retailers: Just Sports, Sports 'N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports 'N Stuff and 650 skateboards at The Sports Dude. The following tables display the per-unit costs for shipping skateboards between the factories and DCs and for shipping skateboards between the DCs and the retailers.

Shipping Costs (per skateboard)

Factory to DC

Factory/DCs

Iowac

Maryland

Idaho

Arkansas

Detroit

$25.00

$25.00

$35.00

$40.00

Los Angeles

$35.00

$45.00

$35.00

$42.50

Austin

$40.00

$40.00

$42.50

$32.50

Shipping Costs (per skateboard)

DC to Retailer

Retailers/DCs

Iowa

Maryland

Idaho

Arkansas

Just Sports

$30.00

$20.00

$35.00

$27.50

Sports 'N Stuff

$27.50

$32.50

$40.00

$25.00

The Sports Dude

$30.00

$40.00

$32.50

$42.50

a) Develop a production and shipping schedule for Sports of All Sorts.

b) What is the minimal transportation cost?