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Due date: 12 April 2021, 23:59 1. A textile company produces two types of silk wearsties and shirts Shirt is a heavier grade of silk cloth and, as such, requires 8.5 pounds of raw silk per yard, whereas tie requires 6 pounds of raw silk per yard. A yard of shirt requires 3.5 hours of processing time: a yard of tie requires 3.2 hours. Although the demand for the is practically unlimited, the maximum demand for shirt is 550 yards per month. The manufacturer has 7500 pounds of silk and 3500 hours of processing time available each month. The manufacturer makes a profit of $2.5 per yard of tie and $3.10 per yard of shirt. The manufacturer wants to know how many yards of each type of wear to produce to maximize profit 1. Formulate a linear programming model for this problem. b. Solve the problem by using excel solver. State the the optimal production mix and objective value. Include the excel file you generate (sensitivity report, answer report, excel model). c. What would be the effect on the optimal solution if company could obtain only 7000 pounds of silk per month? Answer this by using your sensitivity report. 2. Suppose we have a company that sells vehicles. We have three type of vehicles: motorcycle, bilder and car. A motorcycle costs $1,200, a car costs $1700, and a bike costs $800. We sell motorcycles for $1800, car for 52200, and bikes for $1.200 (hint: calculate the net profit by subtracting cost from its selling price). We have $15000 available this month to purchase vehicles. Each vehicle must be assembled; a motorcycle requires 8 hours to assemble, a bike requires 12 hours, and a car requires 16 hours. We estimate that we and our employees have 150 hours available to assemble vehicles. We have enough space in our store to order 25 vehicles this month (assume we wlocate equal spaces for each type of the vehicle). Based on puust sales, we want to stock at least twice s many bikes as the other two combined because bikes sell better. 1. Formulate a linear programming model for this problem b. Solve the linear programming model formulated in part (a) by using the computer. State the optimal solution. Include the excel file you generated (sensitivity report, answer report, excel model). c. Should we try to increase our budget for purchasing vehicles, increspace to stock vehicles of meresse labor bours to assemble vehicles? Why? Answer this by using sensitivity report you obtained 3. A pharmacist blendis four chemicals components into three types of drugs pain pills, blood pills and sleeping pills. The maximum quantities available of each component and the cost per unit e as follows: PS Component Max. Available in grains/day 1 5100 2 2500 3 4200 4 1800 Cost/ $10 8 12 6 To me that each drug keeps certain essential characteristics, the pharmacist has put limits on the percentage of the components in each blend. The limits as well as the selling prices for the various drugs are as follows: The pharmacist wants to produce at least 3000 grams of each drug Drug Component requirement Selling Price Headache Not less than 40% of 1 $15 Not more than 25% of 2 Blood Not less than 20% of 2 18 Not less than 10% of 3 Sleeping Not more than 40% of 2 12 Not less than 15% of 1 Management wishes to determine the optimal mix of the four components that will maximize profit. Formulate a linear programming model for this problem jest formulate it please) 4. Suppose a company releases a new product and wants to follow an effective advertising strategy The company allocates $200000 for advertisement activities Newspapers and TV channels are options to evaluate. The table given below summarizes the member people reached by using with different brands and mediums. New custom Newspaper A 1000 Newspaper B 750 Newspaper 500 10000 TVO TVR Type TVP 500D 2500 Ench newspaper ad costs $2000 and TV ad costs $15000. At most, 10 newspaper ads and 20 TV ads can be purchased. Formulate an LP model for the company to maximize the number of people reached by those ads. (just formulate please) Important Reminder 1: Notice that this homework task requires individual work Your work should be yours and unique. No cheating or you will get a 0 (zero). In addition, no late submission or you will get 0 (zero). Important Reminder 2: You should submit your excel files and solution documents via it- slearning. Alternative ways for submission will not be acepted. Important Reminder 3: Please write clearly 11 cannot read what you write. Teannot grade your work Grading policy for homework: Fach question b 25 point Reference: Ben W Taylor. 2016. Introduction to Mau Scien Pears, Inc USA