The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs.
The total revenue R for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total revenue, we need to know the selling price per unit of the item. To find the total revenue, we multiply this selling price by the number of items produced.
The profit P for a manufacturer is the total revenue minus the total cost. If this number is positive, then the manufacturer turns a profit, whereas if this number is negative, then the manufacturer has a loss. If the profit is zero, then the manufacturer is at a break-even point.
A manufacturer of widgets has fixed costs of $1725 per month, and the variable cost is $40 per widget (so it costs $40 to produce 1 widget). Let N be the number of widgets produced in a month.
(a) Find a formula for the manufacturer's total cost C as a function of N.
C(N) = 40N+1725
(I'm pretty sure this one is right.)
(b) The highest price p, in dollars, of a widget at which N widgets can be sold is given by the formula p = 53 ? 0.01N. Using this, find a formula for the total revenue R as a function of N.
R(N) = 53N
(I'm not sure about this one because it mentions something about p = 53 ? 0.01N...)
(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.
p(N) = 53N - (40N+1725)
(I'm also not sure about this answer because of the above mentioned p = 53 - 0.01N)
(d) Use your formula from part (c) to determine the two break-even points for this manufacturer. Assume here that the manufacturer produces the widgets in blocks of 50, so a table setup showing N in multiples of 50 is appropriate.
____widgets/mo (smaller value)
____widgets/mo (larger value)
(I can't figure this one out because as is... the formula in part (c), as is, is linear and needs to be a parabola... I need help with the inserting of 53 - 0.01N to where the function is a parabola, and thus... I will be able to find the two break even points.)
(e) Use your formula from part (c) to determine the production level at which profit is maximized if the manufacturer can produce at most 1500 widgets in a month. As in part (d), assume that the manufacturer produces the widgets in blocks of 50.
(I'm sure this will come once I can get the formula straight.)
The total revenue R for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total revenue, we need to know the selling price per unit of the item. To find the total revenue, we multiply this selling price by the number of items produced.
The profit P for a manufacturer is the total revenue minus the total cost. If this number is positive, then the manufacturer turns a profit, whereas if this number is negative, then the manufacturer has a loss. If the profit is zero, then the manufacturer is at a break-even point.
A manufacturer of widgets has fixed costs of $1725 per month, and the variable cost is $40 per widget (so it costs $40 to produce 1 widget). Let N be the number of widgets produced in a month.
(a) Find a formula for the manufacturer's total cost C as a function of N.
C(N) = 40N+1725
(I'm pretty sure this one is right.)
(b) The highest price p, in dollars, of a widget at which N widgets can be sold is given by the formula p = 53 ? 0.01N. Using this, find a formula for the total revenue R as a function of N.
R(N) = 53N
(I'm not sure about this one because it mentions something about p = 53 ? 0.01N...)
(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.
p(N) = 53N - (40N+1725)
(I'm also not sure about this answer because of the above mentioned p = 53 - 0.01N)
(d) Use your formula from part (c) to determine the two break-even points for this manufacturer. Assume here that the manufacturer produces the widgets in blocks of 50, so a table setup showing N in multiples of 50 is appropriate.
____widgets/mo (smaller value)
____widgets/mo (larger value)
(I can't figure this one out because as is... the formula in part (c), as is, is linear and needs to be a parabola... I need help with the inserting of 53 - 0.01N to where the function is a parabola, and thus... I will be able to find the two break even points.)
(e) Use your formula from part (c) to determine the production level at which profit is maximized if the manufacturer can produce at most 1500 widgets in a month. As in part (d), assume that the manufacturer produces the widgets in blocks of 50.
(I'm sure this will come once I can get the formula straight.)