A Company Needs to Purchase Several New Machines to Meet $\quad \mathbf { x } _ { \mathrm { i } } =$

question 57

Essay

A company needs to purchase several new machines to meet its future production needs. It can purchase three different types of machines A, B, and C. Each machine A costs $80,000 and requires 2,000 square feet of floor space. Each machine B costs $50,000 and requires 3,000 square feet of floor space. Each machine C costs $40,000 and requires 5,000 square feet of floor space. The machines can produce 200, 250 and 350 units per day respectively. The plant can only afford $500,000 for all the machines and has at most 20,000 square feet of room for the machines. The company wants to buy as many machines as possible to maximize daily production.
Enter the numbers in the appropriate cells of range B5:F10 in the Excel spreadsheet to solve this problem based on the following formulation.
Let $\quad \mathbf { x } _ { \mathrm { i } } =$ mumber of machines of type i purchased
$$\begin{array} { l } 200 X _ { 1 } + 250 X _ { 2 } + 300 X _ { 3 } \\2 \mathrm { X } _ { 1 } + \mathbf { 3 X _ { 2 } } + \mathbf { 5 X _ { 3 } } \leq 20 \\\operatorname { gaX } _ { 1 } + 50 X _ { 2 } + 40 X _ { 3 } \leq 500 \\X _ { 1 } , X _ { 7 } X _ { 3 } \geq 0 \\\end{array}$$

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Definitions:

Water Molecule

A compound consisting of two hydrogen atoms and one oxygen atom bonded together, forming H2O.

Trigonal

Trigonal refers to a molecular geometry where a central atom is surrounded by three other atoms or groups in a plane at 120 degrees to each other.

Planar

Referring to a flat surface or a shape that exists primarily in two dimensions, often used in the context of molecules that lie in a single geometric plane.

Carbon Monoxide

A colorless, odorless, and tasteless gas that is highly toxic, produced by the incomplete combustion of carbon-containing materials.