Date: MAT 1460- Homework Section 3.3 Support your answer by showing your work. 1
ID: 3185639 • Letter: D
Question
Date: MAT 1460- Homework Section 3.3 Support your answer by showing your work. 1. Use the following information to answer a) Find the cost function. the following questions. The marginal cost for producing an item is $12. The fixed costs for the business are $1750. The item sells for $37 b) Find the revenue function. c) Find the profit function. Find the average cost per item when 100 units are produced. d) e) What is the break-even point? 2. Let the supply and demand for radial tires in dollars be given by: Supply: p =-q; Demand: p-81-3q Find the equilibrium quantity and price.Explanation / Answer
1. a).Let x be the number of units of the item produced. Since, the marginal cost is the cost added by producing one additional unit of the item, hence C(x), the cost function is given by C(x) = 12x+1750.
b). The revenue function R(x) is given by R(x) = 37x.
c). The profit function P(x) is given by P(x) = R(x)-C(x) = 37x -12x-1750 = 25x-1750.
d).When 100 units are produced, the average cost per item is (12*100+1750)/100 = 2950/100 = $ 29.50.
e). At the break-even point, we have R(x) = C(x) or, 37x =12x+1750 or, 25x = 1250 so that x = 50. Thus, the break-even point occurs at production and sales of 50 units.
2.The supply and demand for radial tyres is given by Supply: p = 3q/2 and Demand: p = 81-3q/4. At equilibrium, the demand and supply are equal so that 3q/2 = 81-3q/4. or, 3q/2+3q/4 = 81 or, 9q/4 = 81 or, 9q = 81*4 so that q = 81*4/9 = 9*4 = 36. Thus, the equilibrium quantity is 36. Also, the equilibrium price is 3*9/2 = 27/2 = $ 13.50.
3. Let x be the no. of copies made and let the linear model be y = mx+c, where m is the slope and c, the y-intercept( the y-value when x = 0). Here, m = (82-73)/(400-100) = 9/300 = 0.03 so that y = 0.03x+c. Now, on substituting x = 100 and y = 73 in this equation, we get 73= 0.03*100+c or, c = 73-3 = 70. Thus, the linear model required is y = 0.03x +70.The slope is variable cost of printing per copy of the flyer.
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