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Back BUSI $108$ Assignment $6--1.$docx

Instructions:

This assignment has two questions. The full credits are $20.$

Problem $1(10$ points$)$:

Tom opens a plant. The plant can produce two products: a chair and a table. Each chair can earn $$6,$ and each table can earn $$8.$ Each chair costs $2$ hours of labor and $4$ pounds of wood to make, and each table costs $3$ hours and $5$ pounds of wood to make. The plant has $20$ hours of labor and $40$ pounds of wood available. Tom wants to maximize his profits by producing these two types of products. Please formulate this problem using linear programing.

$(1)$ Please define the decision variables in this problem. $(2$ points$).$

$(2)$ Please list the objective function. $(3$ points$)$

$(3)$ Please list all constraints. $(5$ points$)$

Problem $2(10$ points$)$

A company is producing two types of products: bowl and mug. Each bowl needs to have $2$ hours of labor, and $4$ pounds of clay, which can earn $100$ dollars per unit. For each mug, it needs to have $3$ hours of labor, and $1$ pounds of clay, which can earn $20$ dollars per unit. The total number of available labor is $80$ hours, and the total number of available clay is $100$ pounds.

Please use EXCEL SOLVER to find the optimal solutions and the optimal value of the objective function to maximize the earnings.

That is$,$

$($a$)$ What is the optimal number of bowls to produce? $(3$ points$)$

$($b$)$ What is the optimal number of mugs to produce? $(3$ points$)$

$($c$)$ What is the optimal value of the objective function? $(4$ points$)$

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