Mat 540 week 7 homework in excel template
Week 7 Homework
1. Southern Sporting Good Crew effects basketballs and footballs. Each consequence is pied from two suppliess rubber and leather. Each basketball pied results in a avail of $11 and each football earns $15 in avail. The supplies requirements for each consequence and the wholety suppliess conducive are as follows:
Product Supplies Requirements per Individual Rubber (lb.) Leather (ft2 ) Basketball 2.8 3.7 Football 1.5 5.2 Entirety suppliess conducive 600 900
a. Find the optimal separation.
b. What would be the pi on the optimal separation if the avail for the basketball radical from $11 to $12?
c. What would be the pi on optimal separation if 400 concomitant pounds of rubber could be gained? What would be the pi if 600 concomitant clear feet of leather could be gained?
2. A crew results two consequences, A and B, which enjoy avails of $9 and $7, respectively. Each individual of consequence must be processed on two parterre threads, where the required consequenceion terms are as follows:
Product Supplies Requirements per Individual Thread 1 Thread 2 A 11 5 B 6 9 Entirety Hours 65 40
a. Formulate a rectirectirectilinear programming example to enumerate the optimal consequence mix that gain maximize avail.
b. What are the sensitivity ranges for the extrinsic employment coefficients?
c. Enumerate the phantom costs for concomitant hours of consequenceion term on thread 1 and thread 2 and designate whether the crew would choose concomitant thread 1 or thread 2 hours.
3. Formulate and unfold the example for the forthcoming amount: Irwin Textile Mills results two signs of cotton cloth denim and corduroy. Corduroy is a heavier trice of cotton cloth and, as such, requires 8 pounds of raw cotton per yard, when-in-fact denim requires 6 pounds of raw cotton per yard. A yard of corduroy requires 4 hours of processing term; a yard od denim requires 3.0 hours. Although the claim for denim is in-fact unbounded, the apex claim for corduroy is 510 yards per month. The creator has 6,500 pounds of cotton and 3,000 hours of processing term conducive each month. The creator effects a avail of $2.5 per yards of denim and $3.25 per yard of corduroy. The creator omissions to recognize how manifold yards of each sign of cloth to result to maximize avail. Formulate the example and put it into banner shape. Unfold it
a. How greatly extra cotton and processing term are left aggravate at the optimal separation? Is the claim for corduroy met?
b. If Irwin Mills can gain concomitant cotton or processing term, but not twain, which should it excellent? How greatly? Explain your counter-argument.
4. The Bradley parentage owns 410 acres of farmfix in North Carolina on which they gain-ground corn and tobacco. Each acre of corn costs $105 to establish, advance, and harvest; each acre of tobacco costs $210. The Bradleys’ enjoy a budget of $52,500 for contiguous year. The legislation limits the enumerate of acres of tobacco that can be established to 100. The avail from each acre of corn is $300; the avail from each acre of tobacco is $520. The Bradleys’ omission to recognize how manifold acres of each fruit to establish in enjoin to maximize their avail.
a. Formulate the rectirectirectilinear programming example for the amount and unfold.
b. How manifold acres of farmfix gain not be advanced at the optimal separation? Do the Bradleys use the whole 100-acre tobacco parcel?
c. The Bradleys’ enjoy an turn to lease some extra fix from a neighbor. The neighbor is offering the fix to them for $110 per acre. Should the Bradleys’ lease the fix at that cost? What is the apex cost the Bradleys’ should pay their neighbor for the fix, and how greatly fix should they lease at that cost?
d. The Bradleys’ are because gate out a advance to growth their budget. For each dollar they attribute, how greatly concomitant avail would they effect? If they attributeed an concomitant $1,000, would the enumerate of acres of corn and tobacco they establish veer?