Answer:
Maximum profit is $87 when 3 blenders and 11 mixers are produced.
Step-by-step explanation:
let blender is represented by
and and mixer by
.
total time to deliver parts = 24 hrs
total time to assemble = 30 hrs
time taken by each blender to deliver parts = 1 hr
time taken by each mixer to deliver parts = 2 hr
time taken by blenders in final assembling= 2 hr
time taken by mixers in final assembling = 3 hr
Each blender produced nets the firm= $7
Each mixer produced nets the firm= $6
Using this all data linear system of equation will be:
![x_{1} + 2x_{2} =24 ----- (1)\\2x_{1} + 2x_{2} = 30 ----- (2)\\](https://tex.z-dn.net/?f=x_%7B1%7D%20%2B%202x_%7B2%7D%20%3D24%20%20-----%20%281%29%5C%5C2x_%7B1%7D%20%2B%202x_%7B2%7D%20%3D%2030%20-----%20%282%29%5C%5C)
profit function:
![z= 7x_{1} +6x_{2} --- (3)](https://tex.z-dn.net/?f=z%3D%207x_%7B1%7D%20%2B6x_%7B2%7D%20---%20%283%29)
![from (1)\\x_{1} = 0 \implies x_{2}= 12\\x_{2}= 0 \implies x_{1}= 24\\](https://tex.z-dn.net/?f=from%20%281%29%5C%5Cx_%7B1%7D%20%3D%200%20%5Cimplies%20x_%7B2%7D%3D%2012%5C%5Cx_%7B2%7D%3D%200%20%5Cimplies%20x_%7B1%7D%3D%2024%5C%5C)
Coordinate points obtained from (1) are (0,12) and (24,0)
![from (2)\\x_{1}=0 \implies x_{2}=10\\x_{2}=0 \implies x_{1}=15\\](https://tex.z-dn.net/?f=from%20%282%29%5C%5Cx_%7B1%7D%3D0%20%5Cimplies%20x_%7B2%7D%3D10%5C%5Cx_%7B2%7D%3D0%20%5Cimplies%20x_%7B1%7D%3D15%5C%5C)
Coordinate points obtained from (2) are (0,10) and (15,0)
plotting these on graph
points lying in feasible region are:
A(0,0)
B(0,10)
C(3,11)
D(12,0)
substituting these points in (3) to find the maximum profit:
for A (0,0)
z = 0
for B (0,10)
z = 60
for C (3,11)
z = 87
for D (12,0)
z=84
So maximum profit is $87 when 3 blenders and 11 mixers are produced.