Question

In: Math

A business that produces color copies is trying to minimize its average cost per copy​ (total...

A business that produces color copies is trying to minimize its average cost per copy​ (total cost divided by the number of​ copies). This average cost in cents is given by

​f(x)equals=0.00000093x^2−0.0146+60​,

where x represents the total number of copies produced.

​(a) Describe the graph of f.

​(b) Find the minimum average cost per copy and the corresponding number of copies made.

Solutions

Expert Solution

a)

x f(x)
0 60
1000 46.33
2000 34.52
3000 24.57
4000 16.48
5000 10.25
6000 5.88
7000 3.37
7849 2.698925
7900 2.7013
8000 2.72
10000 7
20000 140
30000 459
40000 964
50000 1655
-1000 75.53
-2000 92.92
-3000 112.17
-4000 133.28
-5000 156.25
-6000 181.08
-7000 207.77
-7849 231.8897
-7900 233.3813
-8000 236.32
-10000 299
-20000 724
-30000 1335
-40000 2132
-50000 3115

b)

milcah answered 1 year ago
Next > < Previous

Related Solutions

A corporation is trying to raise money for a business expansion. The total cost of the...
A corporation is trying to raise money for a business expansion. The total cost of the expansion is $1,000,000. The expected return on assets before taxes of the business expansion project is 10% on the total asset investment. (Expected probabilities of returns are .25 of an 8% return, .5 of a 10% return and .25 of a 12% return.) After the privately held corporation owners are considering two options which involve obtaining one of two types of loans from an...
Exercise 1-2. Sunk Cost [LO 2] Rachel Cook owns Campus Copies, a copy business with several...
Exercise 1-2. Sunk Cost [LO 2] Rachel Cook owns Campus Copies, a copy business with several high-speed copy machines. One is a color copier that was purchased just last year at a cost of $25,000. Recently a salesperson got Rachel to witness a demo of a new $23,000 color copier that promises higher speed and more accurate color representation. Rachel is interested but she can’t get herself to trade in a perfectly good copier for which she paid $25,000 and...
Suppose an optimization problem is trying to minimize the cost function : Cost = 7S +...
Suppose an optimization problem is trying to minimize the cost function : Cost = 7S + 10R.   The company is producing two products, product S and product R, subject to the following constraints:                                 S + R ≤ 90                         3S + 10R ≥ 620                         R ≤ 100                         S ≥ 20                         S, R ≥ 0 Program this into a blank Excel worksheet and use Solver to find the solution for S and R such that the objective function is...
1. The long run average total cost shows what happens to average (per unit) total cost...
1. The long run average total cost shows what happens to average (per unit) total cost as a firm grows in size (adds more capital or increases its plant size). True or false? 2. In the short run, at least one input is variable and one input is fixed. True or false? 3. If marginal product is less than average product, average product must be falling. True or false? 4. In the long run, all inputs are variable. True or...
Quantity Total Cost Total Fixed Cost Total Variable Cost Average Fixed Cost Average Total Cost Average...
Quantity Total Cost Total Fixed Cost Total Variable Cost Average Fixed Cost Average Total Cost Average Variable Cost Marginal Cost 0 30 1 75 2 150 3 255 4 380 5 525 6 680 7 840 8 1010 9 1200 Given the quantity and total cost, calculate for total fixed cost, total variable cost, average fixed cost, average total cost, average variable cost, and marginal cost. Excel formulas would be nice but not required.
Illustrate the per unit cost graph. You must include average total cost, average fixed cost, average...
Illustrate the per unit cost graph. You must include average total cost, average fixed cost, average variable cost and marginal cost.
12 - What is target cost per​ unit? A.Target cost per unit is the average total...
12 - What is target cost per​ unit? A.Target cost per unit is the average total unit cost over the​ product's life cycle. B.Target cost per unit is the average total unit cost over the contribution margin ratio. C.Target cost per unit is the contribution margin per unit over the average total unit cost. D.Target cost per unit is the variable unit cost over the​ product's life cycle. 13 - What is value​ engineering? A.Charging different prices to different customers...
Labor Q Total Fixed Cost Total Variable Cost Total Cost Marginal Cost Average Fixed Cost Average...
Labor Q Total Fixed Cost Total Variable Cost Total Cost Marginal Cost Average Fixed Cost Average Variable Cost Average Total Cost 0 0 25 0 1 4 25 25 2 10 25 50 3 13 25 75 4 15 25 100 5 16 25 125 (a) Complete the blank columns. (b)    Assume the price of this product equals $10. What’s the profit-maximizing output (q)?  Note: managers maximize profits by setting MR=MC and under perfectly competitive markets, MR=Price. Thus, maximize profit...
Cowboys Copies, Inc., wants to upgrade its copy machines. Its last update was 2 years ago,...
Cowboys Copies, Inc., wants to upgrade its copy machines. Its last update was 2 years ago, when it spent $1,150 on equipment with an assumed life of 5 years and. The firm uses MACRS depreciation. The old equipment can be sold today for $800. A new system can be installed today for $1,500. This will have a 3 year life and will be depreciated under MACRS 3 year schedule. At the end of 3 years, the new equipment will be...
A friend owns a hotel that gets a lot of seasonal business. The average total cost per day of running the hotel is $75
A friend owns a hotel that gets a lot of seasonal business. The average total cost per day of running the hotel is $75. She tells you that during the off-season (when there are a lot of empty rooms), she had someone offer her $70 for a room. She indignantly tells you she turned the offer down since it was less than her average cost. Was that a good decision? Explain your answer in detail.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT