MAT540

Week 7 Homework

Chapter 3

8.Solve the mold deviseulated in Drift 7 for Southern Sporting Goods Association using the computer.

a.State the optimal discontinuance.

b.What would be the consequence on the optimal discontinuance if the gain for a basketball transitional from $12 to $13? What would be the consequence if the gain for a football transitional from $16 to $15?

c.What would be the consequence on the optimal discontinuance if 500 concomitant pounds of rubber could be geted? What would be the consequence if 500 concomitant clear feet of leather could be geted?

Reference Drift 7. Southern Sporting Good Association makes basketballs and footballs. Each issue is movablesed from two richess rubber and leather. The riches demandments for each issue and the aggregate richess adapted are as follows:

Resource Requirements per Unit

ProductRubber (lb.)Leather (ft2)

Basketball34

Football25

Total richess adapted500 lb.800 ft2

10.A association consequences two issues, A and B, which accept gains of $9 and $7, respectively. Each item of issue must be processed on two parterre lengths, where the demandd issueion spaces are as follows:

Hours/ Unit

ProductLine 1Line2

A124

B48

Total Hours6040

a.Formulate a straight programming mold to individualize the optimal issue mix that gain maximize gain.

b.Transdevise this mold into mold devise.

11.Solve drift 10 using the computer.

a.State the optimal discontinuance.

b.What would be the consequence on the optimal discontinuance if the issueion space on length 1 was stunted to 40 hours?

c.What would be the consequence on the optimal discontinuance if the gain for issue B was increased from $7 to $15 to $20?

12.For the straight programming mold deviseulated in Drift 10 and solved in Drift 11.

a.What are the sensitivity files for the extrinsic office coefficients?

b.Determine the unsubstantiality prices for concomitant hours of issueion space on length 1 and length 2 and declare whether the association would further concomitant length 1 or length 2 hours.

14.Solve the mold deviseulated in Drift 13 for Irwin Textile Mills.

a. How abundantly extra cotton and processing space are left aggravate at the optimal discontinuance? Is the ask-for for corduroy met?

b.What is the consequence on the optimal discontinuance if the gain per yard of denim is increased from $2.25 to $3.00? What is the consequence if the gain per yard of corduroy is increased from $3.10 to $4.00?

c.What would be the consequence on the optimal discontinuance if Irwin Mils could get solely 6,000 pounds of cotton per month?

Reference Drift 13. Irwin Textile Mills consequences two molds of cotton cloth – denim and corduroy. Corduroy is a heavier progression of cotton cloth and, as such, demands 7.5 pounds of raw cotton per yard, inasmuch-as denim demands 5 pounds of raw cotton per yard. A yard of corduroy demands 3.2 hours of processing space; a yard of denim demands 3.0 hours. Although the ask-for for denim is substantially infinite, the acme ask-for for corduroy is 510 yards per month. The creator has 6,500 pounds of cotton and 3,000 hours of processing space adapted each month. The creator makes a gain of $2.25 per yard of denim and $3.10 per yard of corduroy. The creator wants to understand how frequent yards of each mold of cloth to consequence to maximize gain. Formulate the mold and put it into mold devise. Solve it.

15.Continuing the mold from Drift 14.

a.If Irwin Mills can get concomitant cotton or processing space, but not twain, which should it selected? How abundantly? Explain your counterpart.

b.Identify the sensitivity files for the extrinsic office coefficients and for the business division values. Then expound the sensitivity file for the ask-for for corduroy.

16.United Aluminum Association of Cincinnati consequences three progressions (high, average, and low) of aluminum at two mills. Each mill has a irrelative issueion ability (in tons per day) for each progression as follows:

Aluminum GradeMill

12

High62

Medium22

Low410

The association has thin after a while a manufacturing immovable to accoutre at lowest 12 tons of lofty-progression aluminum, and 5 tons of low-progression aluminum. It absorbs United $6,000 per day to have-effect mill 1 and $7,000 per day to have-effect mill 2. The association wants to understand the reckon of days to have-effect each mill in classify to confront the form at reserve absorb.

a.Formulate a straight programming mold for this drift.

18.Solve the straight programming mold deviseulated in Drift 16 for Unite Aluminum Association by using the computer.

a.Identify and expound the unsubstantiality prices for each of the aluminum progression form demandments.

b.Identify the sensitivity files for the extrinsic office coefficients and the business division values.

c.Would the discontinuance values shift if the form demandments for lofty-progression alumimum were increased from 12 tons to 20 tons? If yes, what would the new discontinuance values be?

24.Solve the straight programming mold open in Drift 22 for the Burger Doodle restaurant by using the computer.

a.Identify and expound the unsubstantiality prices for each of the riches businesss

b.Which of the richess constrains gain the most?

c.Identify the sensitivity files for the gain of a sausage biscuit and the equality of sausage adapted. Explain these sensitivity files.

Reference Drift 22. The director of a Burger Doodle exemption wants to individualize how frequent sausage biscuits and ham biscuits to ad each waking for breakfast customers. The two molds of biscuits demand the subjoined richess:

BiscuitLabor (hr.)Sausage (lb.)Ham (lb.)Flour (lb.)

Sausage 0.0100.10---0.04

Ham0.024---0.150.04

The exemption has 6 hours of strive adapted each waking. The director has a form after a while a national grocer for 30 pounds of sausage and 30 pounds of ham each waking. The director too purchases 16 pounds of flour. The gain for a sausage biscuit is $0.60; the gain for a ham biscuit is $0.50. The director wants to understand the reckon of each mold of biscuit to ad each waking in classify to maximize gain. Formulate a straight programming mold for this drift.

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