Purpose of this assignment: After doing this assignment the student should be able:

To identify decision variables in a given business situation.

To formulate objective function in a given business situation.

To translate business criteria into valid mathematical criteria.

To effectively communicate LP problem to Excel Solver.

To solve LP problem using Excel Solver.

To interpret the solution obtained from Excel Solver.

Assignment:

Part A: (MANUFACTURINGSHIPPING COSTS) Steinwelt Piano manufactures upright and console pianos in two plants, Plant I and Plant II. The output of Plant I is at most 300/month, whereas the output of Plant II is at most 250/month. These pianos are shipped to three warehouses, which serve as distribution centers for the company. To fill current and projected future orders, Warehouse A requires at least 200 pianos/month, Warehouse B requires at least 150 pianos/month, and Warehouse C requires at least 200 pianos/month. The shipping cost of each piano from Plant I to Warehouse A, Warehouse B, and Warehouse C is $60, $60, and $80, respectively, and the shipping cost of each piano from Plant II to Warehouse A, Warehouse B, and Warehouse C is $80, $70, and $50, respectively. What shipping schedule will enable Steinwelt to meet the warehouses requirements while keeping shipping costs to a minimum?

Part B: (MANUFACTURINGCOLD FORMULA PRODUCTION) Beyer Pharmaceutical produces three kinds of cold formulas: Formula I, Formula II, and Formula III. It takes 2.5 hours to produce 1000 bottles of Formula I, 3 hours to produce 1000 bottles of Formula II, and 4 hours to produce 1000 bottles of Formula III. The profits for each 1000 bottles of Formula I, Formula II, and Formula III are $180, $200, and $300, respectively. For a certain production run, there are enough ingredients on hand to make at most 9000 bottles of Formula I, 12,000 bottles of Formula II, and 6000 bottles of Formula III. Furthermore, the time for the production run is limited to a maximum of 70 hr. How many bottles of each formula should be produced in this production run so that the profit is maximized?

Part C: (ADVERTISING) As part of a campaign to promote its annual clearance sale, the Excelsior Company decided to buy television advertising time on Station KAOS. Excelsiors advertising budget is $102,000. Morning time costs $3000/minute, afternoon time costs $1000/minute, and evening (prime) time costs $12,000/minute. Because of previous commitments, KAOS cannot offer Excelsior more than 6 min of prime time or more than a total of 25 min of advertising time over the 2 weeks in which the commercials are to be run. KAOS estimates that morning commercials are seen by 200,000 people, afternoon commercials are seen by 100,000 people, and evening commercials are seen by 600,000 people. How much morning, afternoon, and evening advertising time should Excelsior buy to maximize exposure of its commercials

Purpose of this assignment: After doing this assignment the student should be able To identify decisios variables in a given business situation To formulatjective function in a given business station To translate business ceria into valid mathematical criteria To effectively communicate problem to face Scher To solve problem in celover To interpret the solution obtained from DxcelSolver Assignment Part A (MANUFACTURING SHIPPING COSTS Stewet Pano manufactures upright and cool pianos In two plants, Plants and Plant Il. The output of Plantilsat most 300/month, whereas the output of Plant it is at most 250/month. These pianos are shipped to three warehouses, which serve as distribution centers for the company. To till current and projected future orders, Warehouse Arequires at least 200 pianos/month, Warehouse requires at least 350 pianos/month, and Warehouse requires at least 200 pianos/month. The shipping cost of each piano from antite Warehouse Warehouse and Warehouse is $60,560, and $80, respectively, and the shipping cost of each piano romantto Warehouse A Warehouse, and Warehouse is Sao, S70, and $50, respectively. What shipping Schedule will enable Steinwelt to meet the warehouses' requirements while keeping shipping costs to Part B: MANUFACTURING-COLD FORMULA PRODUCTION Beyer Pharmaceutical produces three kinde of cold formulas: Formula Formal and formula takes 2.5 hours to produce 1000 beses of formula 3 hours to produce 1000 bottles of Formula 1 and 4 hours to produce 1000 bottles of Formula in the profits for each 1000 bottles of formula formula it and formulate $180, $200 and 5100, respectively. For a certain production tun, there are enough ingredients on hand to make most 9000 bottles of Formula 32.000 bottles of Formula it and 6000 bottles of Formula Furthermore, the time for the production run is limited to a maximum of 70 hr. How many bottles of each formula should be produced in this production run so that the profitis maximised? Part C (ADVERTISING) As part of a comparto promote itsua clearance sale, the Company decided to buy television writing time on Station KAOS. Excelsior's rising buitis $102,000 Morning time coats $3000/minute, afternoon time costs $100/minute, and evening anime) time costs $12,000/minute. Because of previous commitments, KAOS cannot offer Excelsior more than mino prime time or more than a total of 25 min of advertising time over the week.in which the commercials to be run KAOS estimates that morning commercials are seen by 200.000 people afternoon commercials are seen by 100,000 people, and evening commercials are seen by 60.000 people. How much morning afternoon, and evening advertising time should also buy to maximize exposure of its commercial