Dear Student, I am solving the first question as per HOMEWORKLIB RULES, post multiple questions to get the remaining answers
Question 1:
Number of employees in carpenter department = 1/2 * 150 = 75
Hours available in carpenter department = 75 * 35 = 2625 hours
Number of employees in plastics department = 50
Hours available in plastics department = 50 * 35 = 1750 hours
Number of employees in completion department = 150 - 75 - 50 = 25
Hours available in completion department = 25 * 35 = 875 hours
Let the number of simple canoes be x
Let the number of luxurious canoes be y
Maximize, Profit = 8*x + 10*y
Constraints:
5*x + 5 *y <= 2625 (constraints on labor hours)
2*x+2*y <= 1750 (constraints on plastic department)
2*x+4*y <= 875 (constraints on completion department)
1/3(x+y) <= y <= 2/3(x+y)
1/3x + 1/3y <= y <= 2/3x + 2/3y
x/2 <=y<=2x (hence the number of luxurious boxes must be between half of the ordinary box and not more than two times of the ordinary box).
Solving all the constraint, we get the optimal solution
optimal value of x as 875/4 and optimal value of y as 875/8
So, the company should make 218 ordinary boxes and 109 luxurious boxes for maximizing profit
Note - Post any doubts/queries in comments section
a company which manufactures canoes employs 150 I. A company which manufactures canoes employs 150 employees, each of whom working 35 hours per week. Half of them work in the carpenter d...
a company which manufactures canoes employs 150 I. A company which manufactures canoes employs 150 employees, each of whom working 35 hours per week. Half of them work in the carpenter department, 50 persons in the plastics department, and the rest of them at the completion department. The company manufactures the simple canoes with net unit profit 8 and the luxury canoes with corresponding profit 10. A simple canoe requires 5 hours in the carpenter department and two hours in...
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