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

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.
What are the key formulas for this Excel spreadsheet implementation of the following formulation?
Let $\quad \mathbf { x } _ { \mathrm { i } } =$ mumber of machines of type i purchased

$\begin{array}{ll}\text { MAX: } & 200 \mathrm{X}_{1}+250 \mathrm{X}_{2}+300 \mathrm{X}_{3} \\\text { Subject to: } & 2 \mathrm{X}_{1}+3 \mathrm{X}_{2}+5 \mathrm{X}_{3} \leq 20 \\& 80 \mathrm{X}_{1}+50 \mathrm{X}_{2}+40 \mathrm{X}_{3} \leq 500 \\& \mathrm{X}_{1}, \mathrm{X}_{2} \mathrm{X}_{3} \geq 0\end{array}$