The Supervisor of a Manufacturing Plant Is Trying to Determine

question 31

Essay

The supervisor of a manufacturing plant is trying to determine how many of two parts, Part X and Part Y, are to be produced per day. Each part must be processed in three sections of the plant. The time required for the production along with the profit contribution for each part are given in the following table. $$\begin{array}{l}\begin{array} { l c c c c } &&&\text { Time required (Minutes/Unit) }\\& \text { Section 1 } & \text { Section 2 } & \text { Section 3 } & \text { Profit/Unit } \\\hline \text { Part X } & 50 & 30 & 18 & \$ 2 \\\text { Part Y } & 80 & 45 & 22 & \$ 3 \\\text { Available time (minutes) } & 3600 & 2500 & 1200 &\end{array}\end{array}$$ No more than 60 units of Part X and up to 70 units of Part Y can be produced per day. The company already has orders for 30 units of Part Y that must be satisfied.
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a. Develop a linear programming model and solve the model to determine the optimal production quantities of Parts X and Y.
b. If more time could be made available in Section 2, how much would the profit increase? (Hint: Generate Answer Report).

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Definitions:

Resistant Children

Children who show reluctance or opposition in response to guidance or requests from adults, demonstrating a form of behavioral resistance.

Insecure Attachment

A type of attachment characterized by anxiety, avoidance, or ambivalence, often resulting from inconsistent caregiving and affecting individuals' relationships and emotional well-being.

Maternal Depression

A mood disorder affecting mothers, characterized by persistent feelings of sadness, anxiety, and/or emptiness during pregnancy or after childbirth.

Child Maltreatment

Involves any act by a caretaker that results in harm or potential harm to a child, including physical, sexual, emotional abuse, or neglect.