Instructions:• Do this on a clean sheet of paper (preferably bond paper).• Construct a complete Linear Programming Model.• Show a complete, legible, and well-organized solution.• Upload in Canvas an image or pdf file of your work through this page.1. A businessman needs 5 cabinets, 12 desks, and 18 shelves cleaned out. He has two part-time employees Sue and Janet. Sue can cleanone cabinet, three desks and three shelves in one day, while Janet can clean one cabinet, two desks and 6 shelves in one day. Sue is paid$25 a day, and Janet is paid $22 a day. In order to minimize the cost, how many days should Sue and Janet be employed?2. A factory manufactures two types of gadgets, regular and premium. Each gadget requires the use of two operations, assembly andfinishing, and there are at most 12 hours available for each operation. A regular gadget requires 1 hour of assembly and 2 hours offinishing, while a premium gadget needs 2 hours of assembly and 1 hour of finishing. Due to other restrictions, the company can make atmost 7 gadgets a day. If a profit of $20 is realized for each regular gadget and $30 for a premium gadget, how many of each should bemanufactured to maximize profit?3. In order to produce 1000 tons of non-oxidizing steel for engine valves, at least the following units of manganese, chromium andmolybdenum, will be needed weekly: 10 units of manganese, 12 units of chromium, and 14 units of molybdenum (1. unit is 10 pounds).These metals are obtainable from dealers in nonferrous metals, who, to attract markets make them available in cases of three sizes, S,M and L. One S case costs $9 and contains 2 units of manganese, 2 units of chromium and 1 unit of molybdenum. One M case costs $12and contains 2 units of manganese, 3 units of chromium, and 1 unit of molybdenum. One L case costs $15 and contains 1 unit ofmanganese, 1 unit of chromium and 5 units of molybdenum. How many cases of each kind should be purchased weekly so that theneeded amounts of manganese, chromium and molybdenum are obtained at the smallest possible cost? What is the smallest possible cost?Formulate and solve by linear programming.

As per expert guidelines I am solving only first question.

Answered: 1. A businessman needs 5 cabinets, 12…

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 bakery sells pies and cakes. Each pie costs $2 to produce, requires a half an hour of labor, and sells for $3; while each cake costs $3, requires an hour of labor, and sells for $5. How many pies and cakes, respectively, should be produced in each 8 hour day if the bakery spends no more than $30 per day on supplies?
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both sheets are for the same problem.
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