Question

In: Advanced Math

1.) (15 pts.) Miamiville Interiors is a small shop that produces a variety of items that...

1.) (15 pts.) Miamiville Interiors is a small shop that produces a variety of items that are sold through home improvement departments at local hardware stores. Among the items MI produces are replacement cabinet facings for kitchen and bathroom cabinets. The production manager must decide how many of each of two types of cabinet should be produced in the next production period. The net revenues and demand for each type of cabinet are listed in the table below. Also, in the table are production cost per unit and the units available for each of three types of wood used in the cabinet construction. Revenue per unit Maple Pine Walnut Demand Cabinet A $8 6 11 400 Cabinet B 13 4 9 600 Cost/unit $3.00 $1.80 $3.75 Units Available 400 600 200 Formulate a linear program to determine how many of each of the types of cabinet should be produced, using each type of wood. You seek to maximize profit (revenue – cost), while satisfying demand for the two cabinet styles.

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Expert Solution

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ANSWER:

EXPLANATION:

Let Assume Xij represent the number of cabinets for each type where i = 1,2 and represent the Cabinet A & B and j = 1,2,3 and represent the type of woods.

And simultaneously Yij represent the revenue per unit and Zj represent the cost per unit

X11 = Cabinet A with Maple

X12 = Cabinet A with Pine

X13 = Cabinet A with Walnut

X21 = Cabinet B with Maple

X22 = Cabinet B with Pine

X23 = Cabinet B with Walnut

Objective -

Max Z = Sum of (Xij*Yij) - (X11+X21)*Z1 - (X12+X22)*Z2 - (X13+X23)*Z3

Constraints -

X11 + X21 <= 400

X12 + X22 <= 600

X13 + X23 <= 200

X11 + X12 + X13 >= 400

X21 + X22 + X23 >= 600

Xij >= 0

Below is the screenshot of the LP table in excel -

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I HOPE YOU UNDERSTAND..

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Colby Messinger answered 1 year ago

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