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Breaking Even The background for this exercise can be found in Exercises 15, 16, 17, and 18 in Section 1.4. A manufacturer of widgets has fixed costs of $700 per month, and the variable cost is $65 per thousand widgets (so it costs $65 to produce 1 thousand widgets). Let N be the number, in thousands, of widgets produced in a month Find a formula for the manufacturer’s total cost C as a function of N.
a. Find a formula for the manufacturer’s total cost C as a function of N.
b. The highest price p, in dollars per thousand widgets, at which N can be sold is given by the formula
c. Use your answers to parts a and b to find a formula for the profit p of this manufacturer as a function of N.
d. Use your formula from part c to determine the two break-even points for this manufacturer Assume that the manufacturer can produce at most 500 thousand widgets in a month.
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FUNCTIONS+CHANGE -WEBASSIGN
- Total Cost The background for this exercise can be found in Exercises 13 and 14 in Section 3.2. The following table gives the total cost C, in dollars, for a widget manufacturer as a function of the number N of widgets produced during a month. Number N Total cost C 200 7900 250 9650 300 11, 400 350 13, 150 a. What are the fixed costs and variable cost for this manufacturer? b. The manufacturer wants to reduce the fixed costs so that the total cost at a monthly production level of 350 will be 12, 975. What will the new fixed costs be? c. Instead of reducing the fixed costs as in part b, the manufacturer wants to reduce the variable cost so that the total cost at a monthly production level of 350 will be 12, 975. What will the new variable cost be?arrow_forwardRedo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?arrow_forward
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