MARKETING STRATEGIES Two dentists, Lydia Russell and Jerry Carlton, are planning to establish practices in a newly developed community. Both have allocated approximately the same total budget for advertising in the local newspaper and for the distribution of fliers announcing their practices. Because of the location of their offices, Russell will get
a. Construct the payoff matrix for the game, and show that it is not strictly determined.
b. Find the optimal strategy for both Russell and Carlton.
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Chapter 9 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences
- A manufacturing company receives orders for engines from two assembly plants. Plant I needs at least 45 engines, and plant II needs at least 32 engines. The company can send at most 120 engines to these assembly plants. It costs $30 per engine to ship to plant I and $40 per engine to ship to plant II. Plant I gives the manufacturing company $20 in rebates toward its products for each engine they buy, while plant II gives similar $10 rebates. The manufacturer estimates that they need at least $1500 in rebates to cover products they plan to buy from the two plants. How many engines should be shipped to each plant to minimize shipping costs? What is the minimum cost? How many engines should be shipped to each plant to minimize shipping costs, subject to the given constraints? The number of engines to send to plant I is The number of engines to send to plant II isarrow_forwardTwo dentists, Lydia Russell and Jerry Carlton, are planning to establish practices in a newly developed community. Both have allocated approximately the same total budget for advertising in the local newspaper and for the distribution of fliers announcing their practices. Because of the location of their offices, Russell is expected to get 43% of the business if both dentist advertise only in the local newspaper; if both dentist advertise through fliers, then Russell is expected to get 39% of the business; if Russell advertises exclusively in the local newspaper and Carlton advertises exclusively through fliers, then Russell is expected to get 66% of the business. Finally, if Russell advertises through fliers exclusively and Carlton advertises exclusively in the local newspaper, then Russell is expected to get 58% of the business. (a) Construct the payoff matrix for the game. (Enter each percentage as a decimal.) Carlton Russell N P = F Q= Is the game strictly determined? Yes No N (b)…arrow_forwardA manufacturing company receives orders for engines from two assembly plants. Plant I needs at least 45 engines, and plant Il needs at least 32 engines. The company can send at most 140 engines to these assembly plants. It costs $30 per engine to ship to plant I and $40 per engine to ship to plant II. Plant I gives the manufacturing company $20 in rebates toward its products for each engine they buy, while plant Il gives similar $10 rebates. The manufacturer estimates that they need at least $1500 in rebates to cover products they plan to buy from the two plants. How many engines should be shipped to each plant to minimize shipping costs? What is the minimum cost? How many engines should be shipped to each plant to minimize shipping costs, subject to the given constraints? The number of engines to send to plant Lis The number of engines to send to plant II is wwwarrow_forward
- A manufacturing company receives orders for engines from two assembly plants. Plant I needs at least 45 engines, and plant II needs at least 32 engines. The company can send at most 120 engines to these assembly plants. It costs $30 per engine to ship to plant I and $40 per engine to ship to plant II. Plant I gives the manufacturing company $20 in rebates toward its products for each engine they buy, while plant Il gives similar $15 rebates. The manufacturer estimates that they need at least $1500 in rebates to cover products they plan to buy from the two plants. How many engines should be shipped to each plant to minimize shipping costs? What is the minimum cost? How many engines should be shipped to each plant to minimize shipping costs, subject to the given constraints? The number of engines to send to plant I is The number of engines to send to plant II is What is the minimum shipping cost, subject to the given constraints? $ Next ptsarrow_forwardThe Marketing Club at your college has decided to raise funds by selling three types of T-shirt: one with a single-color "ordinary" design, one with a two-color "fancy" design, and one with a three- color "very fancy" design. The club feels that it can sell up to 400 T-shirts. "Ordinary" T-shirts will cost the club $6 each, "fancy" T-shirts $8 each, and "very fancy" T-shirts $10 each, and the club has a total purchasing budget of $4,000. It will sell "ordinary" T-shirts at a profit of $4 each, "fancy" T-shirts at a profit of $5 each, and "very fancy" T-shirts at a profit of $4 each. How many of each kind of T- shirt should the club order to maximize profit? What is the maximum profit the club can make?arrow_forwardThe Marketing Club at your college has decided to raise funds by selling three types of T-shirt: one with a single-color "ordinary" design, one with a two-color "fancy" design, and one with a three-color "very fancy" design. The club feels that it can sell up to 400 T-shirts. "Ordinary" T-shirts will cost the club $6 each, "fancy" T-shirts $8 each, and "very fancy" T-shirts $10 each, and the club has a total purchasing budget of $4,000. It will sell "ordinary" T-shirts at a profit of $4 each, "fancy" T-shirts at a profit of $5 each, and "very fancy" T-shirts at a profit of $4 each. How many of each kind of T-shirt should the club order to maximize profit? What is the maximum profit the club can make? a. the club should order no "ordinary" T-shirts, no "fancy" T-shirts and 400 "very fancy" T-shirts, the profit is $4,000 O b. the club should order no "ordinary" T-shirts, 400 "fancy" T-shirts and no "very fancy" T-shirts, the profit is $4,000 c. the club should order no "ordinary"…arrow_forward
- A manufacturing company receives orders for vehicle audio systems from two assembly plants in Atlanta and Little Rock. Atlanta needs at least 45 audio systems and Little Rock needs at least 32 audio systems. The company can send at most 140 audio systems to these assemply plants. It costs $33 per system to ship to Atlanta and $40 per system to ship to Little Rock. Atlanta gives the manufacturing company $20 in rebates toward its products for each audio system they buy, while Little Rock gives $13 in rebates. The manufacturer estimates they need at least $1500 in rebates to cover products they plan to buy from the two plants. How many audio systems should be shipped to each plant to minimize shipping costs. What is the minimum cost? Number of audio systems to ship to Atlanta:   Number of audio systems to ship to Little Rock:   Minimum cost: $arrow_forwardBhavika Investments, a group of financial advisors and retirement planners, is providing advice on how to invest $200,000 for one of its clients in the stock market and in money market funds. Each dollar invested in the stock market gives a return of 10% and each dollar invested in money market funds gives a return of 5%. However, there is risk involved: the risk measure for each dollar invested in the stock market is 12, and the risk measure for each dollar invested in the money market is 5. The table below summarizes the information just presented.  Risk measure per investment dollar Percentage return per investment dollar Stock Market 12 10% Money market 5 5% The client has stipulated an annual return of at least $14,000 on his investments in the stock market and money market. Formulate a linear programming model for this situation that will minimize the risk of investing and solve it to find out how much should be invested in each market. check_circlearrow_forwardAdirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank’s planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans. Assume that ASB has the original $1 million in new funds available and that the planning committee has agreed to relax the requirement that at least 40% of the new funds must be allocated to home loans by 1%. How much would the annual return change? How much would the annual percentage return change? Discuss. *arrow_forward
- Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 5% for home loans, 13% for personal loans, and 7% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans. (a) Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the total annual return for the new funds. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". Let H = amount allocated to home loans P = amount allocated to personal loans A = amount allocated to automobile loans Маx H + P + s.t. H + A 2 Minimum Home Loans P + AS Personal Loan…arrow_forwardSouthwest Hospital has an operating room used only for eye surgery. The annual cost of rent, heat, and electricity for the operating room and its equipment is $360,000, and the annual salaries of the people who staff this room total $540,000. Each surgery performed requires the use of $760 worth of medical supplies and drugs. To promote good will, every patient receives a bouquet of flowers the day after surgery. In addition, one-quarter of the patients require dark glasses, which the hospital provides free of charge. It costs the hospital $30 for each bouquet of flowers and $40 for each pair of glasses. The hospital receives a payment of $2000 for each eye operation performed. 1. Identify the revenue per case and the annual fixed and variable costs for running the operating room. 2. How many eye operations must the hospital perform each year in order to break even? 3. Southwest Hospital currently averages about 70 eye operations per month. One of the nurses has just learned about a…arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill