Answer :
Answer: A should be A=200, B should be B=0, and component C should be C=350. This will lead to a maximum profit of$4550.
Explanation:
Let A, B, and C be the number of components of types A, B, and C that the company should manufacture each week. The aim is to maximize the profit. Profit per unit of A, B, and C is $7, $8, and $10, respectively. So, formulate the objective function as follows :MaxP=7A+8B+10C
Based on the calculations, the maximum profit for this small company is equal to $4,400.
How to calculate the maximum profit​?
- Let the fabrication time be x.
- Let the assembly be y.
Next, we would represent the given parameters by using a table as follows:
x y profit
A 2 1 7
B 3 1 8
C 2 2 10
1000 800
From the table above, we subject to have the following system of equations:
2A + 3B + 2C = 1000
A + B + 2C = 800
Mathematically, the maximum profit for this company is given by:
P = 7A + 8B + 10C
By using matrix, the maximum profit and number of electronic components produced per week would be calculated as follows:
[tex]\left[\begin{array}{cccccccc}2&3&2&1&0&0&1000\\1&1&2&0&1&0&800\\-7&-8&-10&0&0&1&0\end{array}\right] \\\\\\\left[\begin{array}{cccccccc}1&2&0&1&-1&0&200\\\frac{1}{2} &\frac{1}{2}&1&0&\frac{1}{2}&0&400\\-2&-3&0&0&5&1&4000\end{array}\right]\\\\\\\left[\begin{array}{cccccccc}\frac{1}{2}&1&0&\frac{1}{2}&-\frac{1}{2}&0&100\\\frac{1}{4} &0&1&\frac{-1}{4}&\frac{3}{4}&0&350\\\frac{-1}{2}&0&0&\frac{3}{2}&\frac{7}{2}&1&4300\end{array}\right][/tex]
[tex]\left[\begin{array}{cccccccc}1&2&0&-1&-1&0&200\\0 &\frac{-1}{2}&1&\frac{-1}{2}&1&0&300\\0&1&0&2&3&1&4400\end{array}\right][/tex]
Thus, we have:
A = 200 components.
B = 0 components.
C = 300 components.
Maximum profit = $4,400.
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