Write the objective function and he constraints Diagram the constraint and identify the feasible region Using the corner point method, identify the production level that meets the objective of maximum profit
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- A manufacturer produces two types of calculator; each requiring material and labour as shown below:
|
Input |
Scientific Calculator |
Graphic Calculator |
Availability |
|
Labour (hrs) |
4 |
5 |
200 |
|
Inspection time |
2 |
1 |
80 |
|
Material (cm2) |
10 |
12 |
600 |
|
PROFIT |
$200 |
$300 |
|
- Write the objective function and he constraints
- Diagram the constraint and identify the feasible region
- Using the corner point method, identify the production level that meets the objective of maximum profit
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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%.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?
- Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?The manager of Jokitian Iron Works Company received an order to produce anumber of pipes which require the use of material A costing $3 and material Bcosting $8 per unit. For each pipe no more than 12 units of Material A and at least16 units of material B must be used. While each unit of A weighs 4 pounds andeach unit of B weighs 6 pounds, the final product must weigh exactly 120 pounds.a. Present the objective function.b. Present the constraint functions.c. Show and label the graph of the feasible solution.d. How many units of each raw material should be used in order to producethe ordered pipes most economically?e. What is the cost of each pipe?Given this linear programming model, solve the model and then answer the questions that follow.Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc.Subject toMachine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hoursMaterials 2x1 + 2x2 + 4x3 ≤ 200 poundsProduct 2 x2 ≤ 16 units x1, x2, x3 ≥ 0 a. Are any constraints binding? If so, which one(s)?
- Only Construct Linear Programming Model for the following Problemb; An individual wishes to invest $9000 over the next year in two typar of inventrent linvestment A yinlds 5% and invertment � yields 8%. Market retearch rocotnenends an allocs tion of at least 25% in A and at most 30% in �. Motsover, investment in A should be at least ball the invertmeut in �. How should the fund be allocated to the two imetrinents?The following table shows the cost to ship goods from Factory 1,2,3 to Warehouse A,B,C: We will designate "F" as the variable for Factory. The constraint that represents the quantity supplied by Factory 1 should be written as: A)F1A+F1B+F1C=500 B)4F1A+6F1B+8F1C<=500 C)F1A+F1B+F1C<=500 D)F1A+F1B+F1C>=500 E)F1A+F2A+F3<=200An investment advisor at RMC Financial Services wants to develop a model that can be used to allocate investment funds among four alternatives: stocks, bonds, mutual funds, and cash. For the coming investment period, the company developed estimates of the annual rate of return and the associated risk for each alternative. Risk is measured between 0 and 1, with higher risk value denoting more volatility and thus more uncertainty. The estimated rate of return for stocks is 10%, for bonds 3%, for mutual funds 4%, and cash 1%. The risk index for the stocks, bonds, and mutual funds investment is estimated as 0.8, 0.2, and 0.3, respectively. Because cash is held in money market funds, the annual return is lower, but it carries essentially no risk (i.e., risk index is zero for cash investment). The objective is to determine the portion of funds allocated to each investment alternatives in order to maximize the total annual return for the portfolio subject to the risk level the client is…
- Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets, Bangladesh and Sri Lanka. Demand for Bicycles in these two markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) a) Determine the company’s total profit function. Also, (i) What are the profit maximizing levels of price and output for the two markets? (ii) Calculate the marginal revenues in each market. b) Now consider two cases: (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging the same price in the two markets what are the profit maximizing levels of price, output, and the total profits?…A healthy diet contains m different nutrients in quantities at least equal to b1, · · · , bm. This diet can be composed by choosing nonnegative quantities x1, · · · , xn of n different foods. One unit quantity of food j contains an amount aij of nutrient i, and has a cost of cj. Formulate this problem as an optimization problem in order to determine the cheapest diet that satisfies the nutritional requirements. What if we want to determine the most nutritious diet that does not exceed the cost given by the different foods? What is the relation between both formulations?