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Linear programming questions (1)

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1.
Print Media Advertising has been given a contract to market Buzz Cola in a major Southern newspaper. Full page ads in the weekday editions (Monday through Saturday) cost $2000, whereas on Sunday a full page ad costs $8000. Daily circulation of the newspaper is 30,000 on weekdays and 80,000 on Sunday. PMA has been given a $40,000 advertising budget for the month of August. The experienced advertising executives at PMA feel that both weekday and Sunday newspaper ads are important, hence, they wish to run the equivalent of at least eight weekday and at least two Sunday ads during August. (Assume that a fractional ad would simply mean that a smaller ad is placed on one of the days; that is 3.5 ads would mean 3 full page ads and one half page ad. Also, assume that smaller ads reduce the exposure and costs proportionally.) This August has 26 weekdays and 5 Sundays. PMA would like to find the placement of ads for the month of August that maximizes cumulative total exposure. a.
Carefully formulate the linear programming model to determine the ad placement strategy. b.
Solve the problem graphically. 2.
An individual wishes to invest $5000 over the next year in two types of investments; investment A and investment B. Investment A yields 5% and investment B yields 8%. Market research recommends an allocation of at least 25% in A and at least 50% in B. Moreover, investment in A should be at least half of the investment in B. How should the fund be allocated to the two investments to yield the largest return? a.
Carefully formulate the linear programming model to determine the investment strategy. b.
Solve the problem graphically. 3.
Blacktop refining extracts minerals from ore mined at two different sites in Montana. Each ton of ore from site 1 contains 20% copper, 20% zinc, and 15% magnesium. Each ton of ore coming from site 2 contains 30% copper, 25% zinc and 10% magnesium. The ore from site 1 costs $90 per ton and the ore from site 2 costs $120 per ton. Blacktop would like to buy enough ore to extract at least 8 tons of copper, 6 tons of zinc and 5 tons of magnesium in the least costly manner. a.
Carefully formulate the linear programming model to determine a plan for Blacktop. b.
Solve the problem graphically. In order to receive full credit for your homework, please make sure to adhere to the following requirements.
Solutions must be typed and presented in the proper order
Please solve each problem on a separate page, and attempt to fit the entire solution on one page.
Problem formulations should include careful definition of decision variables. Please use
1
,
2
for variable names. Write a short description of the meaning of each constraint next to it. (just a word or two is fine).
The graphical solution should include a graph (produced by hand or software such as DESMOS). Label axes. Shade the feasible region. Make sure other parts of the graph are not shaded.
Include a table containing all CPFs (Corner-Point Feasible) and the corresponding objective function value
Clearly state your solution using a sentence that reflects the problem context

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