Reference no: EM131065308
The Delicious Apple Company has orchards in Red City, Golden, and Macville Estimated amounts of apples to be available from the three orchards are the following: Red City, 15,000 bushels; Golden, 12,000 bushels; and Macville, 9,000 bushels. Apple Products Company wants to buy up to 10,000 bushels, for which it will pay $2.90 a bushel. Fruit Processors, Inc., is interested in buying up to 12,000 bushels at $3.20 a bushel. Extragood Fruit Company will buy up to 18,000 bushels at $3.10 per bushel. Delicious Apple Company would like to distribute its apples to the buyers so as to maximize its profits. The costs of shipping form the orchards to the buyers' processing plants are given in the following table. It is acceptable to have fractional bushels.
|
From Orchard
|
Apple Products
|
Fruit Processors
|
Extragood Fruit
|
|
Red City
|
$0.55
|
$0.65
|
$0.45
|
|
Golden
|
$0.40
|
$0.45
|
$0.55
|
|
Macville
|
$0.45
|
$0.45
|
$0.85
|
a) Formulate the linear programming formulation for this problem.
b) Using any linear programming software, solve the problem for the optimal answer and provide the value of the objective function and the variables at optimality. Provide a copy of your linear programming output. In addition to providing this output, you are to specifically identify the value of the objective function and the values of the variables at optimality.
c) Using the sensitivity analysis (ranging) output provided as part of the linear programming output, provide two sensitivity analysis interpretations. Provide one based on the objective function and one based on a constraint. Provide a copy of the sensitivity analysis output supporting your interpretations.
d) Now suppose that Delicious Apple has signed a contract with Extragood Fruit that ensures that Extragood Fruit will receive in total at least as many apples as Fruit Processors. Provide the modification to the linear programming formulation provided in a) for this additional requirement. It is not necessary to solve the linear programming problem for the solution.
e) Write a constraint that will ensure that Apple Products obtains no more than 30% of its total number of bushels from the Golden orchard. You only need formulate this constraint. You do not need to solve the linear programming problem for the solution.
|
What is the principal repayment amount
: You need $11,000 to purchase a used car. Your wealthy uncle is willing to lend you the money as an amortized loan. He would like you to make annual payments for 5 years, with the first payment to be made one year from today. He requires a 6% annual r..
|
|
Evaluating a project for the tiff-any golf club
: You are evaluating a project for The Tiff-any golf club, guaranteed to correct that nasty slice. You estimate the sales price of The Tiff-any to be $490 per unit and sales volume to be 1,000 units in year 1; 900 units in year 2; and 1,325 units in ye..
|
|
Find a 90% confidence interval for the average number
: Assuming that the confidence level remains constant, what sample size is needed to reduce by half the margin of error of the confidence interval in part (a)?
|
|
Total cost of building-calculate amount of interest expense
: On January 1, 2016, the Mason Manufacturing Company began construction of a building to be used as its office headquarters. The building was completed on September 30, 2017. What is the total cost of the building? Calculate the amount of interest exp..
|
|
Provide the value of the objective function and the variable
: Using any linear programming software, solve the problem for the optimal answer and provide the value of the objective function and the variables at optimality. Provide a copy of your linear programming output. In addition to providing this output..
|
|
What is a typical amount of miles traveled
: Draw a cumulative frequency distribution. Forty percent of the buses were driven fewer than how many miles? How many buses were driven less than 850 miles?
|
|
Using the formula and financial calculator methods
: What is the present value of a 7-year annuity of $1,000 per period in which payments come at the beginning of each period? The interest rate is 13 percent. Use Appendix D for an approximate answer, but calculate your final answer using the formula an..
|
|
Private investor values local bakery
: Based on its' growth prospects, a private investor values a local bakery at $750,000. She believes that cost savings having a PV of $50,000 can be achieved by changing staffing levels and store hours. She believes the appropriate liquidity discount i..
|
|
Compute the total purchase cost and annual holding cost
: Compute the- EOQ, total purchase cost, annual holding cost, annual order cost, annual total cost
|