Can You Please Solve this

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HW3.pdf

IE413 1

♣ ♣ ♣ ♣ ♣ ♣ ♣♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ Homework #3

♣ ♣ ♣ ♣ ♣ ♣♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ Part 1. Las Cruces Backpack is a company that produces backpacks primarily for students. They are considering offering some combination of two different models—the Collegiate and the Mini. Both are made out of the same rip-resistant nylon fabric. Las Cruces Backpack has a long-term contract with a supplier of the nylon and receives a 5400 square- foot shipment of the material each week. Each Collegiate requires 3 square feet while each Mini requires 2 square feet. The sales forecasts indicate that at most 1000 Collegiates and 1200 Minis can be sold per week. Each Collegiate requires 45 minutes of labor to produce and generates a unit profit of $32. Each Mini requires 40 minutes of labor and generates a unit profit of $24. Las Cruces Backpack has 35 laborers that each provides 40 hours of labor per week. Management wishes to know what quantity of each type of backpack to produce per week. (a) Formulate a linear programming model (LP) for this problem. Be sure to define your

decision variables! (b) Provide LINDO input to solve the LP model provided in (a)

(c) Provide LINGO input to solve the LP model provided in (a)

(d) Use LINDO (or LINGO) to solve the problem, and describe the optimal solution

briefly in “plain English” (e) Use the graphical method by hand to solve the LP model provided in (a). (f) Use the simplex algorithm to solve the LP model provided in (a) (Show the initial and

each succeeding tableau) Part 2. The marketing department of Las Cruces cell phone manufacturer plans to conduct a telephone survey to determine consumer attitudes toward a new cell phone that is currently under development. In order to have a sufficient sample size to conduct the analysis, they need to contact at least 100 young males (under age 40), 150 older males (over age 40), 120 young females (under age 40), and 200 older females (over age 40). It costs $1 to make a daytime phone call and $1.50 to make an evening phone call (due to higher labor costs). This cost is incurred whether or not anyone answers the phone. The table below shows the likelihood of a given customer type answering each phone call. Assume the survey is conducted with whoever first answers the phone. Also, because of limited evening staffing, at most one-third of phone calls placed can be evening phone calls. How should the marketing department conduct the telephone survey so as to meet the sample size requirements at the lowest possible cost?

IE413 2

Who Answers? Daytime Calls Evening Calls

Young Male 10% 20%

Older Male 15% 30%

Young Female 20% 20%

Older Female 35% 25%

No Answer 20% 5%

(a) Formulate a linear programming model (LP) for this problem. Be sure to define your

decision variables! (b) Use LINDO (or LINGO) to solve this model and describe the optimal solution briefly

in “plain English” Part 3. Mr. & Mrs. Smith have run the family farm for over thirty years. They are currently planning the mix of crops to plant on their 120-acre farm for the upcoming season. The table below gives the labor hours and fertilizer required per acre, as well as the total expected profit per acre for each of the potential crops under consideration. Dwight, Hattie, and their children can work at most 6,500 total hours during the upcoming season. They have 200 tons of fertilizer available. What mix of crops should be planted to maximize the family’s total profit?

Crop

Labor Required (hours per acre)

Fertilizer Required (tons per acre)

Expected Profit (per acre)

Oats 50 1.5 $500

Wheat 60 2 $600

Corn 105 4 $950

(a) Formulate a linear programming model (LP) for this problem. Be sure to define your

decision variables! (b) Use LINDO (or LINGO) to solve this model and describe the optimal solution briefly

in “plain English”