e. How many footballs of each type should Supersport produce to maximize the total profit contribution?
f. Which constraints are binding?
g. Interpret the slack and/or surplus in each constraint.
h. Interpret the ranges of optimality for the profit contributions of the three footballs.

Supersport Footballs, Inc., has to determine the best number of All-Pro (A), College (C), and High School (H) models of footballs to produce in order to maximize profits. Constraints include production capacity limitations (time available in minutes) in each of three departments (cutting and dyeing, sewing, and inspection and packaging) as well as a constraint that requires the production of at least 1000 All-Pro footballs. The linear programming model of Supersport's problem is shown here:

See attached sheet for programming model.

a. Overtime rates in the sewing department are $12 per hour. Would you recommend that the company consider using overtime in that department? Explain.
b. What is the dual price for the fourth constraint? Interpret its value for management.
c. Note that the reduced cost for H, the High-School football, is zero, but H is not in the solution at a positive value. What is your interpretation of this value?
d. Suppose that the profit contribution of the College ball is increased by $1. How do you expect the solution to change?
e. How many footballs of each type should Supersport produce to maximize the total profit contribution?
f. Which constraints are binding?
g. Interpret the slack and/or surplus in each constraint.
h. Interpret the ranges of optimality for the profit contributions of the three footballs.

Answer Questions 2 and 3 based on the following LP problem.
Maximize 2X1 + 5X2 + 4X3 Total Profit
Subject to X1 + X2 + X3 > 150 At least a total of 150 units of all three products needed
X1 + 3X2 + 2X3 â?¤ 300 Resource 1
2X1 + X2 + 2X3 â?¤ 250

Consider the following linear program.
MaximizeProfit = 20X + 8Y
Subject to: X + Y < 12 Constraint #1
X + 3Y < 27 Constraint #2
4X + 2Y < 40 Constraint #3
X, Y > 0

We are given the following linear programming problem:
Mallory furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in

Problem #5:
The Southern Sporting Goods Company makes basketballs and footballs. Each product is produced from two resources - rubber and leather. The resource requirements foreach product and thetotal resources available are as follows.
Resource Requirements per unit
Product Rubber (lb) Leather ( ft2 )
Basket

Below is the computer solution to a linear programming problem linear programming:
Forthe above information, answer the following:
a) What arethe objective function and theconstraints?
b) What arethe values of the variables at optimality and what is the value of the objective function at optimality?
c) If ther

Linear Programming Question:
A Southern Oil Company produces two grades of gasoline; Regular and Premium. Theprofitcontributionsare $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline con

Kite 'N String manufacture old-fashioned diagonal and box kites from high-strength paper and wood. Each diagonal kite nets the company a $3 profit, requires 8 square feet of paper and 5 feet of wood. Each box kite nets $5, requires 6 square feet of paper and 10 feet of wood. Each kite is packaged in similar containers. This week

A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows.
Hours/Unit
Product Line 1 Line 2
A 12 4
B 4

Baseball Inc produces Regular gloves and Catcher?s mitt. The linear programming problem is listed below:
Max 5R + 8C
s.t.
R + 3C < or equal to 1800 Cutting dept
3R + 2C < or equal to 1800 Finishing dept
R + 2C < or equal to 800 Packaging dept
R, C, > or equal to 0
The computer solution obtained using the Mana