Competencias en la primera infancia

using 1 unit of chemicals and 2 units of compound. Only 800 units of chemicals and 1000 units of the compound are available. The profits available per unit of A and B are respectively Rs.30/- and Rs.20/-.

a. Find the optimal solution to the problem using graphical method.

b. Discuss the sensitivity of the above solution to changes in the profit contributions of the products and availability of resources

2. In a carpentry shop it was found that 100 sq feet of ply wood scrap and 80 square feet of white pine scrap are in usable form for construction of tables and book-cases. It takes 16 sq feet of plywood and 8 sq feet of white pine to make a table. 12 sq feet of plywood and 16 sq feet of white pine are required to construct a book-case. A profit of Rs.25 on each table and Rs.20 on each book case can be realized. How can the left over wood be most profitably used? Use graphical method to solve the problem.

a. Find the optimal solution to the problem using graphical method.

b. Discuss the sensitivity of the above solution to changes in the profit contributions of the products and availability of resources.

3. M/S BM Electric co. produces two types of electric dryers A and B that are produced and sold on weekly basis. The weekly production quantity cannot exceed 25 units for A and 35 for B due to limited resources. The company employs 60 workers. Dryer A requires two man-weeks of labor whereas B requires only one man-hr. Profit earned by A is Rs.60/-and B is Rs.40/-. Formulate the above as a linear programming problem and graphically solve for maximum profit.

4. A manufacturer produces two different models X & Y of the same product. Model X makes a contribution of Rs.50/- per unit and model Y, Rs.30/- per unit towards total profit. Raw materials R1 & R2 are required for production. At least 18 kg of R1 and at least 12 kg of R2

must be used daily. Also at most 34 hours of labour are to be utilized.

A quantity of 2 kg of R₁is required for X and 1 kg of R₁is required for

Y. For each of X & Y, 1 kg of R2 is required. It takes 3 hrs to manufacture X and 2 hours to manufacture Y. How many units of each model should be produced to maximize the profit?

5. A company manufactures two types of belts A & B. The profits are Rs. 0.40/- &Rs. 0.30/- per belt respectively. Time required for manufacturing A is twice the time required for B. If the company were to manufacture only B type of belts they could make 1000 units per day. Leather available for production is only worth 800 belts per day (A & B combined). Belt A requires a fancy buckle availability of which is restricted to 400 units per day. Buckles required for B are available only 700 per day. What should the daily production plan be for belts A & B? Formulate the above problem as LPP and solve by graphical method.

6. An advertising agency wishes to reach two types of audiences, customers with monthly incomes greater than Rs 15,000/- (target audience A) and customers with monthly incomes less than Rs 15,000/- (target audience B). The total advertising budget is Rs.2, 00, 000 /-. One programme of TV advertising costs Rs. 50, 000/-.

One programme of radio advertising costs Rs.20, 000/-. For contract reasons at least 3 programmes ought to be on TV and number of radio programmes must be limited to 5. A survey indicates that a single TV programme reaches 4, 50, 000 customers in target audience A and 50, 000 in target audience B. One radio programme reaches 20, 000 customers in target audience A and 80,000 in target audience B.

Determine the media mix to maximize the total reach.

7. A dealer wishes to purchase a number fans and sewing machines. he has only Rs.5760/- to invest and has space utmost for 20 items. A fan costs him Rs 360 and a sewing machine Rs 240. His expectation is that he can sell a fan at a profit of Rs 22 and sewing machine at a profit of Rs 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit? Formulate this problem as linear programming problem and then use graphical method to solve it.

8. The inmates of an institution are daily fed two food items A & B. To maintain their health the nutritional requirements for each individual and the nutrient content of each food item are given. The problem is to determine the combination of units of A & B per person at minimum cost. When per unit cost of A & B is given as below

FOOD A FOOD B MINIMUM DAILY

REQUIREMENT

CALCIUM 10 UNITS 4 UNITS 20 UNITS

PROTEIN 5 UNITS 5 UNITS 20 UNITS

CALORIES 2 UNITS 6 UNITS 12 UNITS

PRICE IN

RUPEES

0.6 1.00

9. Ashok Chemicals Company Manufactures two chemicals A & B which are sold to the manufacturers of soaps & detergents. On the basis of the next month’s demand the management has decided that the total production for chemicals A & B should be 350 kilograms.

Moreover a major customer’s order of 125 kilograms for product A also must be supplied. Product A requires 2 hrs of processing time per kilogram and product B requires one hr of processing time per kilogram. For the coming month 600 hrs of processing time is available. The company wants to meet the above requirements at minimum total production cost. The production costs are Rs2/- per kilogram for product A and Rs3/- for B. Ashok chemicals company wants to determine its optimal product mix and the total minimum cost relevant to the above. Formulate the above as a linear programming problem. Solve the problem with graphical method. Does the problem have multiple optimal solutions?

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LINEAR PROGRAMMING MODEL –