2.A Spanish manufacturer has produced a new range of expensive leather briefcases. A Swiss retailer is considering placing an order
...
considering placing an order for 300 of each design. The Sales Manager and Chief Buyer negotiate the contract.
Student A.
You are the Sales Manager for the Spanish briefcase manufacturer.
You want the retailer to agree the following:
Delivery time: Four weeks after receiving order
Place of delivery: The retailer's main warehouses in Zurich and Geneva
Price: Top-of-the range briefcase: €550
Medium-priced briefcase: €320
Colours: Black and brown
Payment: By bank transfer when goods have been dispatched
Discount: 4% for orders over 100
Returns: Medium-priced briefcases (easier to resell)
Student B
You are the Chief Buyer for the Swiss retailer.
You want the manufacturer to agree to the following:
Delivery time: Two weeks after receiving order
Place of delivery: Individual retail outlets (16 around the country)
Price: Top-of-the-range briefcase: €500
Medium-priced briefcase: €270
Colours: Black, brown, maroon, pink
Payment: Two months after delivery
Discount: 10% for orders over 200
Returns: All unsold briefcases returnable up to one year after order
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4.A manufacturer of bicycles builds 1-, 3- and 10-speed models. The bicycles are made of both aluminum and steel. The
...
uminum and steel. The company has available 38 comma 160 units of steel and 48 comma 380 units of aluminum. The 1-, 3-, and 10-speed models need, respectively, 8, 12 and 16 units of steel and 15, 10, and 20 units of aluminum. The company makes $4 per 1-speed bike, $6 per 3-speed, and $16 per 10-speed. Use the simplex method to complete parts (a) and (b).
(a) How many of each type of bicycle should be made in order to maximize profit? What is the maximum profit?
Set up the linear programming problem. Let x 1, x 2, and x 3 represent the numbers of 1-, 3-, and 10-speed bicycles, respectively, and let z be the total profit.
▼
Minimize
Maximize
zequals
nothing
subject to
8 x 1 plus 12 x 2 plus 16 x 3
▼
greater than
less than or equals
greater than or equals
less than
nothing
15 x 1 plus 10 x 2 plus 20 x 3
▼
greater than
less than or equals
less than
greater than or equals
nothing
x 1greater than or equals0, x 2greater than or equals0, x 3greater than or equals0.
(Do not factor. Do not include the $ symbol in your answers.)
Set up the initial simplex tableau and use the Simplex Method to solve.
The maximum profit is $
nothing. To get that profit, the company should make
nothing 1-speed bicycle(s),
nothing 3-speed bicycle(s), and
nothing 10-speed bicycle(s).
(Type whole numbers.)
(b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A.
When the profit is maximized, all of the steel is used but
nothing units of aluminum remain unused.
(Type a whole number.)
B.
When the profit is maximized, some of each material remains unused. Specifically,
nothing units of aluminum and
nothing units of steel remain unused.
(Type whole numbers.)
C.
When the profit is maximized, all of the available aluminum and steel is used.
D.
When the profit is maximized, all of the aluminum is used but
nothing units of steel remain unused.
(Type a whole number.)
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