Answered: 1. A biologist is developing two new… | bartleby

1. A biologist is developing two new strains of bacteria. Each sample of Type A bacteria produces five new viable bacteria and each Type B bacteria produces six new viable bacteria. Altogether, at least 150 new viable bacteria must be produced. At least 10, but not more than 20 of the original sample must be Type A and not more than 60 of the samples must be Type B. A sample of Type A costs ₱500 and a sample of Type B costs ₱700. If both types are to be used, how many surplus of each type should be used to minimize the cost?

Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 93P: This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits...

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Formulate an LP model for the following problems.
1. A biologist is developing two new strains of bacteria. Each sample of Type A bacteria
produces five new viable bacteria and each Type B bacteria produces six new viable
bacteria. Altogether, at least 150 new viable bacteria must be produced. At least 10,
but not more than 20 of the original sample must be Type A and not more than 60 of
the samples must be Type B. A sample of Type A costs ₱500 and a sample of Type B
costs ₱700. If both types are to be used, how many surplus of each type should be
used to minimize the cost?

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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.
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%.

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