Homework SourseA softdrink manufacturer can produce 1200 cases of soda in a
A soft-drink manufacturer can produce 1200 cases of soda in a week at a total cost of $7300, and 1700 cases of soda at a total cost of $9000. Each case of soda will sell for $12.60.
TYPE ANSWER!!!
a) Write the cost function. Identify the manufacturer’s weekly fixed costs and marginal cost per case of soda to be produced.
b) Find the total cost of producing 500 cases of soda
c) How many cases of soda will the manufacturer have to sell in order to break even?
d) How many cased of soda will need to be sold in order to make a profit of $1380? (round to the nearest case)
TYPE ANSWER!!!
Solution
(a) Let the soda manufacturer’s fixed weekly cost be $a and let the marginal cost be $ b per case. Now,1200 cases of soda can be produced in a week at a total cost of $7300 so that a +1200b = 7300…(1). Further, 1700 cases of soda can be produced in a week at a total cost of $ 9000 so that a +1700b = 9000…(2). Now, on subtracting the 2nd equation from the 1st equation, we get a +1700b- a -1200b = 9000-7300 or, 500b = 1700 so that b = 1700/500 or, b= 3.40. On substituting this value of b in the 1st equation, we get a+1200*3.40 = 7300 or, a +4080 = 7300 so that a = 7300-4080 or, a = 3220. Thus,the soda manufacturer’s fixed weekly cost is $ 3220 and the marginal cost is $ 3.40 per case. Further, if C(x) is the cost of producucing x soda cases in a week, then C(x) = 3220+3.40 x.
(b) The total cost of producing 500 cases of soda in a week is 3220+500*3.40 = 3220+1700 =$ 4920.
(c) Each case of soda sells for $12.60. If the soda manufacturer breaks even on producing and selling x cases of soda in a week, then the revenue = cost so that 12.60x = 3220+3.40x or, 12.60x-3.40x = 3220 or, 9.2x = 3220 so that x = 3220/9.2 = 350. Thus, the soda manufacturer breaks even on producing and selling 350 cases of soda in a week.
(d) Let x cases of soda be sold to make a profit of $ 1380 in a week. Then 12.60 x = 3220+3.40x +1380 or, 9.2x = 4600 so that x = 4600/9.2 = 500. Thus, the soda manufacturer will make a profit of $ 1380 (in a week) on producing and selling 500 cases of soda in a week.
