Advertisements
Advertisements
प्रश्न
A manufacturer produces bulbs and tubes. Each of these must be processed through two machines M1 and M2. A package of bulbs requires 1 hour of work on Machine M1 and 3 hours of work on M2. A package of tubes requires 2 hours on Machine M1 and 4 hours on Machine M2. He earns a profit of ₹ 13.5 per package of bulbs and ₹ 55 per package of tubes. If maximum availability of Machine M1 is 10 hours and that of Machine M2 is 12 hours, then formulate the L.P.P. to maximize the profit.
Advertisements
उत्तर
Let the manufacturer produce ‘x’ packages of bulbs and ‘y’ packages of tubes.
The profit on a package of bulbs is ₹ 13.5 and that of tubes is ₹ 55.
∴ Total profit = ₹ (13.5 x + 55y)
We construct a table with the constraints of machines M1 and M2 as follows:
| Machine\Product | Bulbs x |
Tubes y |
Maximum Availability in hours |
| M1 | 1 | 2 | 10 |
| M2 | 3 | 4 | 12 |
From the table, the total time required on M1 is (x + 2y) hours and on M2 is (3x + 4y) hours.
∴ The constraints are:
x + 2y ≤ 10, 3x + 4y ≤ 12
Since x and y cannot be negative, we have x ≥ 0, y ≥ 0
∴ Given problem can be formulated as follows:
Maximize Z = 13.5x + 55y
Subject to x + 2y ≤ 10, 3x + 4y ≤ 12, x ≥ 0, y ≥ 0.
APPEARS IN
संबंधित प्रश्न
Find the feasible solution of the following inequation:
3x + 4y ≥ 12, 4x + 7y ≤ 28, y ≥ 1, x ≥ 0.
The point of which the maximum value of x + y subject to the constraints x + 2y ≤ 70, 2x + y ≤ 95, x, ≥ 0, y ≥ 0 is is obtained at ______.
Solution of LPP to minimize z = 2x + 3y, such that x ≥ 0, y ≥ 0, 1 ≤ x + 2y ≤ 10 is ______.
The corner points of the feasible solution given by the inequation x + y ≤ 4, 2x + y ≤ 7, x ≥ 0, y ≥ 0 are ______.
If the corner points of the feasible solution are (0, 0), (3, 0), (2, 1), `(0, 7/3)` the maximum value of z = 4x + 5y is ______.
The half-plane represented by 3x + 2y < 8 contains the point ______.
Solve the following LPP:
Maximize z = 4x + 2y subject to 3x + y ≤ 27, x + y ≤ 21, x ≥ 0, y ≥ 0.
Find graphical solution for the following system of linear in equation:
3x + 4y ≤ 12, x - 2y ≥ 2, y ≥ - 1
Solve the following LPP:
Maximize z = 4x1 + 3x2 subject to
3x1 + x2 ≤ 15, 3x1 + 4x2 ≤ 24, x1 ≥ 0, x2 ≥ 0.
Solve the following LPP:
Maximize z =60x + 50y subject to
x + 2y ≤ 40, 3x + 2y ≤ 60, x ≥ 0, y ≥ 0.
Solve the following LPP:
Minimize z = 4x + 2y
Subject to 3x + y ≥ 27, x + y ≥ 21, x + 2y ≥ 30, x ≥ 0, y ≥ 0
Objective function of LPP is ______.
Fill in the blank :
A dish washing machine holds up to 40 pieces of large crockery (x) This constraint is given by_______.
State whether the following is True or False :
Saina wants to invest at most ₹ 24000 in bonds and fixed deposits. Mathematically this constraints is written as x + y ≤ 24000 where x is investment in bond and y is in fixed deposits.
State whether the following is True or False :
The point (1, 2) is not a vertex of the feasible region bounded by 2x + 3y ≤ 6, 5x + 3y ≤ 15, x ≥ 0, y ≥ 0.
The feasible region is the set of point which satisfy.
Maximize z = 5x + 2y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0
Maximize z = 7x + 11y subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0
Maximize z = 10x + 25y subject to x + y ≤ 5, 0 ≤ x ≤ 3, 0 ≤ y ≤ 3
Minimize z = 2x + 4y is subjected to 2x + y ≥ 3, x + 2y ≥ 6, x ≥ 0, y ≥ 0 show that the minimum value of z occurs at more than two points
Maximize z = −x + 2y subjected to constraints x + y ≥ 5, x ≥ 3, x + 2y ≥ 6, y ≥ 0 is this LPP solvable? Justify your answer.
A company produces two types of pens A and B. Pen A is of superior quality and pen B is of lower quality. Profits on pens A and B are ₹ 5 and ₹ 3 per pen respectively. Raw materials required for each pen A is twice as that of pen B. The supply of raw material is sufficient only for 1000 pens per day. Pen A requires a special clip and only 400 such clips are available per day. For pen B, only 700 clips are available per day. Formulate this problem as a linear programming problem.
Solve the following linear programming problems by graphical method.
Minimize Z = 3x1 + 2x2 subject to the constraints 5x1 + x2 ≥ 10; x1 + x2 ≥ 6; x1 + 4x2 ≥ 12 and x1, x2 ≥ 0.
A firm manufactures two products A and B on which the profits earned per unit are ₹ 3 and ₹ 4 respectively. Each product is processed on two machines M1 and M2. Product A requires one minute of processing time on M1 and two minutes on M2, While B requires one minute on M1 and one minute on M2. Machine M1 is available for not more than 7 hrs 30 minutes while M2 is available for 10 hrs during any working day. Formulate this problem as a linear programming problem to maximize the profit.
The maximum value of Z = 3x + 5y, subject to 3x + 2y ≤ 18, x ≤ a, y ≤ 6, x, y ≥ 0 is ______.
The optimal value of the objective function is attained at the ______ of feasible region.
The set of feasible solutions of LPP is a ______.
Two kinds of foods A and B are being considered to form a weekly diet. The minimum weekly requirements of fats, Carbohydrates and proteins are 12, 16 and 15 units respectively. One kg of food A has 2, 8 and 5 units respectively of these ingredients and one kg of food B has 6, 2 and 3 units respectively. The price of food A is Rs. 4 per kg and that of food B is Rs. 3 per kg. Formulate the L.P.P. and find the minimum cost.
