19.03.2023 - 14:36

Your local cell phone company offers you a choice of billing plans: Plan A: Pay 5 cents per call. Plan B: Pay an initial $2.00 a week, which allows you up to 30 calls per week at no charge. Any additional call over 30 costs 5 cents per call. Plan C: Pay a

Question:

Your local cell phone company offers you a choice of billing plans:

Plan A: Pay 5 cents per call.

Plan B: Pay an initial $2.00 a week, which allows you up to 30 calls per week at no charge. Any additional call over 30 costs 5 cents per call.

Plan C: Pay an initial $4.00 a week, which allows you up to 80 calls per week at no charge. Any additional call over 80 costs 4 cents per call.

If your budget for keeping in touch is $12 per week, graph your budget constraints under the three plans. (Make sure you label the budget constraint for each plan properly.)

Answers (1)
  • FunkyDrunkyMonkey
    April 3, 2023 в 02:00

    To graph your budget constraints for the three plans, we need to first find out the maximum number of calls we can make under each plan within the budget of $12 per week.

    For Plan A, each call costs 5 cents, so we can make 240 calls per week with a budget of $12. Therefore, the budget constraint for Plan A is a straight line with a slope of -0.05 (since each additional call costs 5 cents) and a y-intercept of 240 (since we can make 240 calls with $12).

    For Plan B, we can make 30 calls per week at no charge, so we only need to pay for additional calls. To maximize the number of calls we can make within a budget of $12, we should make 30 calls and then use the remaining budget to make additional calls at a cost of 5 cents each. This gives us a total of 30 + (12 - 2)/0.05 = 250 calls per week. Therefore, the budget constraint for Plan B is a straight line with a slope of -0.05 (for additional calls over 30) and a y-intercept of 250 (since we can make 250 calls with $12).

    For Plan C, we can make 80 calls per week at no charge, so we only need to pay for additional calls. To maximize the number of calls we can make within a budget of $12, we should make 80 calls and then use the remaining budget to make additional calls at a cost of 4 cents each. This gives us a total of 80 + (12 - 4)/0.04 = 380 calls per week. Therefore, the budget constraint for Plan C is a straight line with a slope of -0.04 (for additional calls over 80) and a y-intercept of 380 (since we can make 380 calls with $12).

    We can now graph the budget constraints for the three plans on the same set of axes, with the number of calls on the x-axis and the cost on the y-axis. The budget constraint for Plan A is a straight line passing through the point (0, 240) and with a slope of -0.05. The budget constraint for Plan B is a straight line passing through the point (0, 250) and with a slope of -0.05 for additional calls over 30. The budget constraint for Plan C is a straight line passing through the point (0, 380) and with a slope of -0.04 for additional calls over 80. The graph should look something like this:

    Budget constraints graph for the three phone plans

    The shaded area under each budget constraint represents the set of feasible choices for that plan. To compare the three plans, we can look for the plan that gives us the highest number of calls within our budget of $12 per week. From the graph, we can see that Plan C gives us the highest number of calls (380) within our budget, followed by Plan B (250), and then Plan A (240). Therefore, Plan C would be the best choice if our goal is to maximize the number of calls we can make within a budget of $12 per week.

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