A farmer has 300 acres of available land and $60,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c).Profits and Constraints for CropsPotatoesCornx2$160$60Number of AcresCost (per acre)Profit (per acre)(a) Give the dual problem.subject to:X₁$400$180withW = y₁ +Y₁ + 400y2Y₁ + 160y₂Y21806090Planting acres of potatoes,(Simplify your answers.)CabbageX3$280$90VI VI IIY₁ + 280y₂Y₁ ≥ 0, y₂ ≥0>(b) The solution to the dual problem can be interpreted as shadow profits. Use shadow profits to estimate the farmer's profit if land is cut to 270 acres but capital increases to $63,000.The farmer's estimated profit is $(Simplify your answer.)acres of corn, and=Total300$60,000Z(c) Suppose the farmer has 330 acres of land but only $57,000. Find the optimum profit and the planting strategy that will produce this profit.acres of cabbage will produce an optimal profit of $¯.

Given LP- Max Profit (W) = 180x1 + 60x2 + 90x3S.t. -400x1 + 160x2 + 280x3≤57000 (Cost…

Answered: A farmer has 300 acres of available…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 123P

See similar textbooks

Similar questions

If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.
Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company experts to estimate product demand. Then we use Excels trend curve fitting capabilities to fit a quadratic function that represents that segments demand function. Finally, we add the segment demand curves to derive an aggregate demand curve. Try this procedure for pricing a candy bar. Assume the candy bar costs 0.55 to produce. The company plans to charge between 1.10 and 1.50 for this candy bar. Its marketing department estimates the demands shown in the file P07_47.xlsx (in thousands) in the three regions of the country where the candy bar will be sold. What is the profit-maximizing price, assuming that the same price will be charged in all three regions?

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

SEE MORE TEXTBOOKS