47x + 31y = 63 31x + 47y = 15
1 answer:
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Answer:
Step-by-step explanation:
Using the Excel Formula:
Decision Variable Constraint Constraint
A 65 65 100
B 80 80 80
C 90 90 90
14100 300 300
= (150 *B3)+(80*B4) +(65*B5)-(100-B3+80-B4+90-B5)*90
Now, we have:
Suppose A, B, C represent the number of units for production A, B, C which is being manufactured
A B C Unit price
Need of X 2 1 1 $20
Need of Y 2 3 2 $30
Need of Z 2 2 3 $25
Price of
manufac - $200 $240 $220
turing
Now, for manufacturing one unit of A, we require 2 units of X, 2 units of Y, 2 units of Z are required.
Thus, the cost or unit of manufacturing of A is:
$20 (2) + $30(2) + $25(2)
$(40 + 60 + 50)
= $150
Also, the market price of A = $200
So, profit = $200 - $150 = $50/ unit of A
Again;
For manufacturing one unit of B, we require 1 unit of X, 3 units of Y, and 2 units of Z are needed and they are purchased at $20, $30, and 425 each.
So, total cost of manufacturing a unit of B is:
= $20(1) + $30(3) + $25(2)
= $(20 + 90+50)
= $160
And the market price of B = $240
Thus, profit = $240- $160
profit = $80
For manufacturing one unit of C, we have to use 1 unit of X, 2 unit of Y, 3 units of Z are required:
SO, the total cost of manufacturing a unit of C is:
= $20 (1) + $30(2) + $25(3)
= $20 + $60 + $25
= $155
This, the profit = $220 - $155 = $65
However; In manufacturing A units of product A, B unit of product B & C units of product C.
Profit --> 50A + 80B + 65C
This should be provided there is no penalty for under supply of there is under supply penalty for A, B, C is $40
The current demand is:
100 - A
80 - B
90 - C respectively
So, the total penalty
This should be subtracted from profit.
So, we have to maximize the profit
Subject to constraints;
we have the total units of X purchased can only be less than or equal to 300 due to supplies capacity
Then;
due to 2A, B, C units of X are used in manufacturing A, B, C units of products A, B, C respectively.
Next; demand for A, B, C will not exceed 100, 80, 90 units.
Hence;
and because they are positive quantities
The objective is:
A, B, C Decision Varaibles;
Constraint are: