A cargo ship is loaded with two types of cargo. Each container of cargo A is 400 cubic feet involume, weighs 10,000 lbs and earns $11,000 in profit. Each container of cargo B is 300 cubic feetin volume, weighs 20,000 lbs, and earns $9,000 in profit. The ship can carry no more than 30,000cubic feet in volume and no more than 1,000,000 lbs. How many containers of each type shouldbe carried to maximize the profit?Let x be the number of containers of cargo A and y be the number of containers of cargo B.What is the objective function of this linear programming problem?P = 400x + 10,000yP = 300x + 20,000yP = 11,000x + 9,000yP =400x + 300yP = 10,000x + 20,000y

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Answered: A cargo ship is loaded with two types…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A farmer has 12 hectares of land on which he grows corn, wheat, and soybeans. It costs $4500 per hectare to grow corn, $6000 to grow wheat, and $5000 to grow soybeans. Because of market demand the farmer will grow twice as many hectares of wheat as corn. He has allocated $6,375,000.00 for the cost of growing his crops. How many hectares of each crop should he plant?
An online retailer requires three different size containers to package its products for shipment. The costs of these containers A, B, and C, and their capacities are shown as follows: Container A B C Cost ($ each) 4 6 7 Capacity (cu in) 200 400 600 If the retailer orders 2500 containers with a total capacity of 1,100,000 cu in at a cost of $15,000, how many of each are in the order?
A company makes three components for sale. The components are processed on two machines: a shaper and a grinder. The time required. (in minutes) on each machine are as follows: Component Shaper Time Grinder Time A 6 4 B 4 5 C 4 2 The shaper is available for 7200 min. and grinder for 6600 min. No more than 200 units of component C can be sold, but up to 1000 units of each of the other components can be sold. In fact the company has orders for 600 units of component A that must be satisfied. The profit contributions for components A, B and C are $8, $6 and $9 respectively. Formulate the problem for deciding the production quantities. Solve the problem using Excel Solver. Run the sensitivity analysis report in Excel Solver. What are the objective coefficient ranges (Range of Optimality) for each coefficient. Interpret these. What are the dual prices for each constraint? Interpret these. What are the right-hand side ranges (Range of Feasibility)? Interpret them. If more time is…
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The total mass of some watermelons and mangoes is 132.3 kg. The total mass of the mangoes is 35.1 kg more than the total mass of the watermelons. There are five times as many mangoes as watermelons. Each watermelon has a mass of 1.18 kg more than each mango. (a) What is the mass of all the watermelons in kilograms? (b) What is the mass of each mango in kilograms?
both sheets are for the same problem.
A famine relief effort is being mounted and there are three types of food bundles that can be flown out during each delivery. Bundle 1 has 4 kg. of flour, 4 kg. of sugar and 12 litres of water. Bundle 2 has 12 kg. of flour, 4 kg. of sugar and 4 litres of water and Bundle 3 has 8 kg. of flour, 8 kg. of sugar and 8 litres of water. The relief agency has 5200 kg. of flour, 3792 kg. of sugar and 6000 litres of water for each shipment. Bundle 1 can provide for 10 people between deliveries, Bundle 2 for 8 people and Bundle 3 for 11 people. How many bundles of each type should the relief agency send on each flight in order to maximize the number of people being fed. Do this problem by setting up a linear programming problem and determining the vertices of the feasibility set. Enter the number of bundles of types 1, 2, and 3 (in that order) into the answer box below, separated with commas.

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