Question

The Highlands Craft Store is a small craft operation that employs local artisans to produce clay bowls and mugs. Two primary resources used by the company are special pottery clay and skilled labor. Each bowl requires four pounds of clay and 1 hour of labor. Each mug requires 3 pounds of clay and 2 hours of labor. There are 2 workers working 16 hours per day and 240 pounds of clay is available each day. The firm has commitments for 75 mugs. Each bowl sells for $40 and each mug for $50.

Formulate as a linear program problem.

Answer 1

Answer: Let x₁ and x₂ be the number of bowl and mug to be manufactured.
Objective Function: The sale price of per unit of bowl and mug is $40 and $50 respctively. Since objective of the firm is to maximize the profit, therefore, the objective function is given by
Maximize: Z = 40x₁ + 50x₂

Condition 1: The Highlands Craft Store uses special pottery clay and skilled labor. We have 32 working hours from 2 laborers who work for 16 hours a day and 240 pounds of clay. As per the given data, the clay constraints can be formulated as given below:

4x₁ + 3x₂ = 240
x₁ + 2x₂ = 32

Condition 2: Atleast 75 mugs (x₂) should be produced.

x₂ 75

Combining all the conditions, the linear programming problem becomes:
Maximise Z = 40x₁ + 50x₂
Subject to constraints :
4x₁ + 3x₂ = 240
x₁ + 2x₂ = 32
x₂ 75
x₁ 0