a Problem 1-12 (Algorithmic) The O\'Neill Shoe Manufacturing Company will produc
ID: 3327976 • Letter: A
Question
a
Problem 1-12 (Algorithmic)
The O'Neill Shoe Manufacturing Company will produce a special-style shoe if the order size is large enough to provide a reasonable profit. For each special-style order, the company incurs a fixed cost of $1200 for the production setup. The variable cost is $40 per pair, and each pair sells for $50.
Let x indicate the number of pairs of shoes produced. Develop a mathematical model for the total cost of producing x pairs of shoes. Express your answer in terms of x.
TC = _______
Let P indicate the total profit. Develop a mathematical model for the total profit realized from an order for x pairs of shoes. Express your answer in terms of x.
P = _____
How large must the shoe order be before O'Neill will break even? Round your answer to the nearest whole number.
x = ______
Problem 1-15 (Algorithmic)
Preliminary plans are under way for the construction of a new stadium for a major league baseball team. City officials have questioned the number and profitability of the luxury corporate boxes planned for the upper deck of the stadium. Corporations and selected individuals may buy the boxes for $300,000 each. The fixed construction cost for the upper-deck area is estimated to be $4,500,000, with a variable cost of $125,000 for each box constructed.
a. What is the breakeven point for the number of luxury boxes in the new stadium? Round your answer to the nearest whole number.
Breakeven point = ______ luxury boxes
b. Preliminary drawings for the stadium show that space is available for the construction of up to 45 luxury boxes. Promoters indicate that buyers are available and that all 45 could be sold if constructed. What is your recommendation concerning the construction of luxury boxes?
In order to maximize profits, the recommendation is to build 45 luxury corporate boxes .
What profit is anticipated? Round your answer to the nearest dollar.
Profit = $ _______
Problem 2-41
Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $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 contains 0.6 gallons of grade A crude oil. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery used to produce the gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons.
Formulate a linear programming model that can be used to determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize total profit contribution. If required, round your answers to two decimal places.
What is the optimal solution?
What are the values and interpretations of the slack variables? If an amount is zero, enter "0".
What are the binding constraints?
Demand for premium__________
Problem 2-49
PharmaPlus operates a chain of 30 pharmacies. The pharmacies are staffed by licensed pharmacists and pharmacy technicians. The company currently employs 85 full-time-equivalent pharmacists (combination of full time and part time) and 175 full-time-equivalent technicians. Each spring management reviews current staffing levels and makes hiring plans for the year. A recent forecast of the prescription load for the next year shows that at least 250 full-time-equivalent employees (pharmacists and technicians) will be required to staff the pharmacies. The personnel department expects 10 pharmacists and 30 technicians to leave over the next year. To accommodate the expected attrition and prepare for future growth, management states that at least 15 new pharmacists must be hired. In addition, PharmaPlus’s new service quality guidelines specify no more than two technicians per licensed pharmacist. The average salary for licensed pharmacists is $40 per hour and the average salary for technicians is $10 per hour.
Determine a minimum-cost staffing plan for PharmaPlus. How many pharmacists and technicians are needed?
The optimal solution requires full-time equivalent pharmacists and full-time equivalent technicians. The total cost is $ per hour.
Given current staffing levels and expected attrition, how many new hires (if any) must be made to reach the level recommended in part (a)?
What will be the impact on the payroll?
The payroll cost will ___ by $ _____ per hour.
Problem 2-24
Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher’s model. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table:
Assuming that the company is interested in maximizing the total profit contribution, answer the following:
What is the linear programming model for this problem? If you don't need the variable in the model, enter "0". If you need a negative number, enter minus sign with it. If necessary, enter the numbers as a common fraction.
Let R = number of units of regular model.
C = number of units of catcher’s model.
Select the correct graph that reflects the optimal solution. The optimal solution will state how many gloves of each model Kelson should manufacture.
What is the total profit contribution Kelson can earn with the given production quantities? If required, round your answer to the nearest dollar.
$
How many hours of production time will be scheduled in each department? If required, round your answers to the nearest whole number.
What is the slack time in each department? If required, round your answer to the nearest whole number. If no entry is required, enter "0" or leave the box blank.
Problem 2-25
George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund. Whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 7.5%.
Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. If required, round your answers to three decimal places.
Solve the problem. If required, round your answers to one decimal place.
Optimal solution: B =____ , S = ____
Value of optimal solution is _____ %
Explanation / Answer
Probem 1-2
The O'Neill Shoe Manufacturing Company will produce a special-style shoe if the order size is large enough to provide a reasonable profit. For each special-style order, the company incurs a fixed cost of $1200 for the production setup. The variable cost is $40 per pair, and each pair sells for $50.
Let x indicate the number of pairs of shoes produced. Develop a mathematical model for the total cost of producing x pairs of shoes. Express your answer in terms of x.
TC = _______
x : number of pairs of shoes produced
Fixed cost : production setup = $1200
Variable cost = $ 40 per pair
Total cost of producing x pairs of shoes = fixed cost + x x variable cost = 1200 + 40 x x = 1200 + 40x
Total cost of producing x pairs of shoes = 1200 + 40x
TC = 1200 + 40x
Let P indicate the total profit. Develop a mathematical model for the total profit realized from an order for x pairs of shoes. Express your answer in terms of x.
P = _____
x : Number of pairs of shoes
Selling price of one pair of shoe = $50
Selling prrice of x pairs of shoes = 50x
Profit : P = Selling price of x pairs of shoes - Total cost of producing x pairs of shoes
P = 50 x - (1200 + 40x) = 50x - 1200 - 40x = 10x -1200
P = 10x -1200
How large must the shoe order be before O'Neill will break even? Round your answer to the nearest whole number.
x = ______
Break even means profit is zero ; therefore O'Neill will break even if P =0
P = 10x -1200 = 0
10x = 1200; x= 1200/10 = 120
x= 120
Shoe order must be atleast 120 pairs for O'Neill to break even
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.