Question

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 each of the other two departments. The working hours for each luxury canoe are 5, 2 and 4 at the carpenter department, plastics department and completion department respectively. Marketing calculations have shown that not less than 1/3 and not more than 2/3 of the total number of the canoes should be luxurious. How will the company maximize its overall net profit? Given the LP: Max Z = 4x, + 2x2 +3x +x, + x, 2. with 2x, +x, +2x, + x, 15 3x,+4x2 +x,+2x, S10 x,20,i=1,5 a- Determine the corresponding dual problem of Z. b- Using graphically method to find the solution of problem a c- From results of b-, determine the x 1...x5 to obtain the maximize value of Z. 3. There are three warehouses (1, 2, 3) and three markets (A,B,C). The supplies and demands of the warehouses and markets are given in following table. The costs of supplying each item is also given in this table. 10 150 175 275 12 Demand 200 a- Formulate the problem as linear programming. b- Solve this problem to minimize the transportation cost. 4. Consider the linear programming problem: Find yi and y2 to minimize yity2 subject to th 100 300 constraints yı+2yz232 yity225 y220. Graph the constraint set and solve

Answer 1

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