MAT540 Week 7 HomeworkP8, P10, P11, P12, P14, P15
1. Southern Sporting Good Firm makes basketballs and footballs. Every product is produced from two assets rubber and leather-based. The useful resource necessities for every product and the complete assets out there are as follows: Useful resource Necessities per Unit Product Rubber (lb.) Leather-based (ft2) Basketball three four Soccer 2 5 Whole assets out there 500 lb. 800 ft2 a. State the optimum answer. b. What could be the impact on the optimum answer if the revenue for a basketball modified from $12 to $13? What could be the impact if the revenue for a soccer modified from $16 to $15? c. What could be the impact on the optimum answer if 500 extra kilos of rubber may very well be obtained? What could be the impact if 500 extra sq. ft of leather-based may very well be obtained? 2. An organization produces two merchandise, A and B, which have earnings of $9 and $7, respectively. Every unit of product have to be processed on two meeting traces, the place the required manufacturing instances are as follows: Hours/ Unit Product Line 1 Line2 A 12 four B four eight Whole Hours 60 40 a. Formulate a linear programming mannequin to find out the optimum product combine that can maximize revenue. b. Rework this mannequin into commonplace kind. three. Resolve drawback 2 utilizing the pc. a. State the optimum answer. b. What could be the impact on the optimum answer if the manufacturing time on line 1 was lowered to 40 hours? c. What could be the impact on the optimum answer if the revenue for product B was elevated from $7 to $15 to $20? four. For the linear programming mannequin formulated in Drawback 2 and solved in Drawback three. a. What are the sensitivity ranges for the target perform coefficients? b. Decide the shadow costs for added hours of manufacturing time on line 1 and line 2 and point out whether or not the corporate would like extra line 1 or line 2 hours. 5. Formulate and clear up the mannequin for the next drawback: Irwin Textile Mills produces two sorts of cotton fabric – denim and corduroy. Corduroy is a heavier grade of cotton fabric and, as such, requires 7.5 kilos of uncooked cotton per yard, whereas denim requires 5 kilos of uncooked cotton per yard. A yard of corduroy requires three.2 hours of processing time; a yard of denim requires three.zero hours. Though the demand for denim is virtually limitless, the utmost demand for corduroy is 510 yards per thirty days. The producer has 6,500 kilos of cotton and three,000 hours of processing time out there every month. The producer makes a revenue of $2.25 per yard of denim and $three.10 per yard of corduroy. The producer needs to know what number of yards of every sort of material to supply to maximise revenue. Formulate the mannequin and put it into commonplace kind. Resolve it. . a. How a lot further cotton and processing time are left over on the optimum answer? Is the demand for corduroy met? b. What's the impact on the optimum answer if the revenue per yard of denim is elevated from $2.25 to $three.00? What's the impact if the revenue per yard of corduroy is elevated from $three.10 to $four.00? c. What could be the impact on the optimum answer if Irwin Mils may receive solely 6,000 kilos of cotton per thirty days? 6. Persevering with the mannequin from Drawback 5. a. If Irwin Mills can receive extra cotton or processing time, however not each, which ought to it choose? How a lot? Clarify your reply. b. Establish the sensitivity ranges for the target perform coefficients and for the constraint amount values. Then clarify the sensitivity vary for the demand for corduroy.