A Company Has Three Treatments That It Can Apply Three

question 52

Essay

A company has three treatments that it can apply three different types of clothes namely denims, linens and suiting yielding the profit $4, $5, and $8 per bolt respectively. One bolt of denims requires 2 hours in Treatment 1, 3 hours in Treatment 2 and 4 hours in Treatment 3. Similarly one bolt of linens requires 3 hours in Treatment 1, 2 hours in Treatment 2 and 4 hours in Treatment 3 while one bolt suiting requires 2 hours in Treatment 1, 3 hours in Treatment 2 and 4 hours in Treatment 3. In a week, total run time of each department is 80 hours, 90 hours, and 65 hours for Treatment 1, Treatment 2 and Treatment 3 respectively.
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Formulation
Let
​
D₁ number of bolts of denims with Treatment 1
D₂ number of bolts of denims with Treatment 2
D₃ number of bolts of denims with Treatment 3
.
.
.
S₃ number of bolts of Suiting with Treatment 3
Max $4(DW + DI + DP) + $5(LW + LI + LP) +$8(SW + SI + SP)
s.t.
​
2D₁ + 3L₁ + 3S₁ ≤ 80
3D₂ + 2L₂ + 3S₂ ≤ 90
4D₃ + 4L₃ + 3S₃ ≤ 65
D₁, D₂, D₃, …, S₃ ≥ 0

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Definitions:

Secondary Growth

This is the process in plants that results in the thickening of stems and roots, mainly due to the activity of the vascular cambium and cork cambium.

Xylem

The vascular tissue in plants responsible for the conduction of water and nutrients from the roots to other parts of the plant.

Palisade Mesophyll

A layer of closely packed photosynthetic cells under the epidermis in leaves, responsible for the absorption of light necessary for photosynthesis.

Spongy Mesophyll

A layer of loosely arranged cells in a plant leaf, facilitating gas exchange and containing chloroplasts for photosynthesis.