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  *A pharmaceutical Company has 100 kg of A, 180 kg of B and 120 kg of C available per month. They can use these materials to make three basic pharmaceutical products namely 5 - 10 - 5, 5 - 5 - 10 and 20 - 5 - 10, where the numbers in each case represent the percentage by weight of A, B and C respectively in each of the products and the balance represents inert ingredients. The cost of these raw mater also are given below : Ingredient Cost per kg (Rs.) Mat A 80 Mat B 20 Mat C 50 Inert ingredients 20 Selling prices of these products are Rs. 40.5, Rs. 43 and Rs. 45 per kg. Respectively. There is a capacity restriction of the company for the product 5 - 10 - 5 ; so as they cannot produce more than 30 kg per month. Formulate a linear programming model for maximising the monthly profit. Determine how much of each of the products they should produce in order to maximize their monthly profit.   * Noah’s Boats makes three differ  ent kinds of boats. All can be made profitably in this company, but the company’s only production is constrained by the limited amount of labour, wood and screws available each month. The director will choose the combination of boats that maximizes his revenue in view of the information given in the following table Input Row Boat Canoe Kayak Monthly availability Labour (Hours) 12 7 9 1,260 hours Wood (Board feet) 22 18 16 19,008board feet   Screws (Kg.) 2 4 3 396 Kg. Selling price (in Rupees) 4,000 2,000 5,000 (i) Formulate the above as a linear programming problem. (ii)solve it by the simplex method.   From the optimal table of the solved linear programming problem, answer the following questions : (iii)How many boats of each type will be produced and what will be the resulting revenue ? (iv)Which, if any, of the resources are not fully utilised ? If so, how much of spare capacity is left ? (v)How much wood will be used to make all of the boats given in the optimal solution ? *The table given below has been taken from the solution procedure of a transportation problem, involving minimization of cost (In Rupees): (i) Show that the above solution in not optimal. (ii) Find an optimal solution. (iii) Does the problem have multiple optimal solutions? Give reasons. If so, find one more optimal solution. (iv) Comment upon the managerial significance of multiple optimal solutions. (v) If it is considered necessary to transport 20 units from factory to stockiest Z, what will be the least-cost distribution schedule and the effect on cost? (vi) If the transport cost from factory A to stockiest Z is increased by Rs 5 per unit, will the solution change? If so, find the new solution.   *The following table gives one of the possible solution to a transportation problem involving three sources and four destinations: (i) is the above solution degenerate? (ii) is the above solution optimal? Is it a unique solution? If yes, why? (iii) what is the opportunity cost of transporting one unit from source S1 to destination D4? (iv) How would the cost be affected if it is decided to transport one unit from S2 to D2? *Suggest the optimal assignment schedule for the following assignment problem: Sale (Rs in Lakh) Markets Salesmen I II III IV  A 80 70 75 72 B 75 75 80 85 C 78 78 82 78 What will be the total maximum sale? *Purchase Manager has decided to place orders for minimum quantity of 500 Nos. of a particular item in order to get a discount of 10%. From the records; it was found out that in the last year, 8 orders each of size 200 Nos. have been placed. Given ordering cost=`500 per order, inventory carrying cost=40% of the inventory value and the cost per unit=`400, is the Purchase Manager  justified in his decision? What is the effect of his decision to the Company?   *Obtain the optimal order quantity using the information giver here:  Annual requirement: 1 million units Ordering and processing cost: 28.80 per order Holding cost: 20% of the unit cost *A shopkeeper has a uniform demand of an item at the rate of 50 units per month. He buys the item from the supplier at the cost of Rs 6 per unit and the cost of placing an order is Rs 10 every time. If the stock holding cost is 20% p.a. Of the stock value, how frequently should he replenish his book? Further. Discount of 10% on the orders exceeding or equal to 1000 units. It is advisable foe the shopkeeper to avail either of these discount offers? *In planning a project to introduce a new product in market, a company lists the various activities, their normal times and costs, and their crash times and cost. They are:  Activity Immediate  predecessor Normal Crash Time(weeks) Cost(Rs) Time(weeks) Cost(Rs)  A - 5 10000 4 12000 B - 2 6000 2 6000 C A 4 8000 3 10000 D A 4 10000 3 15000 E A 3 11000 1 16000 F C 1 7000 1 7000 G D 4 8000 2 12000 H B, H 5 9000 3 12000 I H 2 8500 2 8000
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