i need the answer quickly Q3) Southern Sporting Goods Company makes basketballs, soccer balls, and footballs.Each product is produced from three main materials-rubber, leather, and cotton (forlining) and processed in a machine that is available for 500 minutes. All finishedproducts are stored in the warehouse until the shipment. The material requirements,processing time, and volume requirements for each product are displayed in the tablebelow.Total resourceavailableBasketballs Socer balls FootballsRubber (Ib)31.52.5350Leather (sq. ft.)Lining (sq. ft.)Machine processingStorage space (ft)2.523.535022.52400342.550015681200Each basketball and soccer ball produced results in a profit of $10 and $9, and eachfootball earns $11 in profit. The manager developed a mathematical model and solvedit using excel solver. Answer the following questions based on the excel solversensitivity report below. Assume that the decision variables are continuous.iriable CellsFinalReduced ObjectiveAllowableAllowableCellNameValueCostCoefficient IncreaseDecreaseSC$13 Production: BasketballsSO$13 Production: SoccerballsSE$13 Production: Footballs30.3225806582.9032258130.9677419410 10.02941176 0.8611111119 1.823529412 2.3846153851.9375 4.0595238111AnstraintsFinalShadow ConstraintAllowableAllowableValue292.7419355350329.8387097CellNamePriceRH. SideIncrease350350 131.4814815 57.14285714400 1E+30 70. 16129032500 131.8181818 197.69230771200 417.6470588 261.1111111Decrease1E+30 57.25806452SG$6 Rubber (Ib) UsageSGS7 Leather (sq. t.) UsageSG$8 Lining (aq, R.) UsageSGS9 Machine processing time (min) UsageSGS10 Storage space () Usage2.250012000.1a. Defining the number of basketballs, soccer balls, and the football produced as thedecision variables, formulate the objective function and constraints.b. What would be the change in the profit, if the available rubber drops to 340pounds?c. What is the range for the profit from basketball that keeps the current solutionoptimal?d. If either one additional sq. ft. of leather or one additional sq. ft. of cotton lining isbeing added to the current resources, what would your decision be? What would theeffect of this decision on the profit be?e. The available machine processing time of 500 minutes includes 420 minutes ofregular time and 80 minutes of overtime. Given that the cost of over time is $50.00,would you agree with the manager's decision of having over time? Why?f. Given the prices of the resources reported by the excel solver and resourcesrequired to produce one soccer ball, what is the total value of resources used toproduce one soccer ball?g. Would you consider extending the storage space? How much are you willing topay for an additional ft3 of space?h. Assume that SSGC is now considering producing softballs. It requires 2 lbs. ofrubber, 3 sq. ft. of leather, 2 sq. ft. of cotton lining to produce one softball and ittakes 3 minutes of machine time to process. It requires 10 ft3 in storage space. Theprofit from a softball is expected to be $10.5. How many softballs would youproduce?i. Given the mathematical formulation in part a, define variables for the dualproblem and formulate objective function and constraints.

Part (A): Decision Variable:Suppose-B be the no. of units of basketballs to be producedS be the no.…

Q3) Southern Sporting Goods Company makes basketballs, soccer balls, and footballs. Each product is produced from three main materials-rubber, leather, and cotton (for lining) and processed in a machine that is available for 500 minutes. All finished products are stored in the warehouse until the shipment. The material requirements, processing time, and volume requirements for each product are displayed in the table below. Total resource ETTTT Basketballs Soccer balls Footballs 2.5 available 350 Rubber (Ib) Leather (sq. ft.) Lining (sq. ft.) Machine processing Storage space (ft=) 3 1.5 2.5 3.5 350 2 2.5 2 400 3 2.5 500 15 8 1200 Each basketball and soccer ball produced results in a profit of $10 and $9, and each football earns $11 in profit. The manager developed a mathematical model and solved it using excel solver. Answer the following questions based on the excel solver sensitivity report below. Assume that the decision variables are continuous. wiable Cells Final Reduced Objective Allowable Cost Allowable Decrease 10 10.02941176 0861111111 9 1.823529412 2.384615385 4.05952381 Cell Name Value 30.32258065 82.90322581 Coefficient Increase SC$13 Production: Basketballs SDS13 Production: Soccerballs SES13 Production: Footballs 30 96774194 11 1.9375 nstraints Final Value 292.7419355 350 329 8387007 Shadow Constraint Allowable RH. Side 350 Allowable Decrease 1E+30 57.25806452 350 131.4814815 57.14285714 1E+30 70.16129032 500 131.8181818 197.6023077 1200 417.6470588 261.1111111 Price Cell SG$6 Rubber (b) Usage SGS7 Leather (sq .) Usage SG$8 Lining (sq R.) Usage SG$9 Machine processing time (min) Usage SG$10 Storage space () Usage Name Increase 2.2 400 500 1200 0.1 a. Defining the number of basketballs, soccer balls, and the football produced as the decision variables, formulate the objective function and constraints. b. What would be the change in the profit, if the available rubber drops to 340 pounds? c. What is the range for the profit from basketball that keeps the current solution optimal? d. If either one additional sq. ft. of leather or one additional sq. ft. of cotton lining is being added to the current resources, what would your decision be? What would the effect of this decision on the profit be? e. The available machine processing time of 500 minutes includes 420 minutes of regular time and 80 minutes of overtime. Given that the cost of over time is $50.00, would you agree with the manager's decision of having over time? Why? f. Given the prices of the resources reported by the excel solver and resources required to produce one soccer ball, what is the total value of resources used to produce one soccer ball?