Calculus homework?
BUS 305
Calculus Unit Assignment 1
Description: Problems dealing with functions and other basic algebra concepts and their application to business scenarios.
General Instructions: Because of the notation involved, the questions for this assessment are in this Word document. Work out your answers on paper and choose the letter of the best answer, then go to the Assignments folder in Blackboard and mark the correct answer for each question.
1. Solve this inequality for x
5x – 6 > 2x + 15
a. x < 7
b. x > 7
c. x > 3
d. x < -3
2. Simplify
a. 
b. 
c. 
d. 
3. Simplify
a. 
b. 
c. 
d. 
4. Solve this equation for x.
2x2 – 3x – 5 = 0
a. x = 5 or x = -0.5
b. x = 2.5 or x = -1
c. x = 0.5 or -5
d. x = -2.5 or x = 1
5. Find 
where x = 4 and
a. 90
b. 32
c. 22
d. 14
6. Annual revenue for a company is given by this formula
where R(t) is the annual revenue for year t. What is the annual revenue for year 4?
a. -2
b. 16
c. 38
d. 48
Use this information for questions 7 – 10.
An analyst examined cost and volume data for twenty different production runs. It appears there is a linear relationship between volume (x) and cost (y) so the analyst used simple linear regression to find the equation of the relationship to predict cost. The regression results are
| SUMMARY OUTPUT | ||||||||||||||
| Regression Statistics | ||||||||||||||
| Multiple R | 0.9910 | |||||||||||||
| R Square | 0.9820 | |||||||||||||
| Adjusted R Square | 0.9810 | |||||||||||||
| Standard Error | 1232.83 | |||||||||||||
| Observations | 20 | |||||||||||||
| ANOVA | ||||||||||||||
|
| df | SS | MS | F | Significance F | |||||||||
| Regression | 1495800034 | 1495800034 | 984.17 | 0.0000 | ||||||||||
| Residual | 18 | 27357466.17 | 1519859.231 | |||||||||||
| Total | 19 | 1523157500 |
|
|
| |||||||||
|
| Coefficients | Standard Error | t Stat | P-value | ||||||||||
| Intercept | 14427 | 572.6863 | 25.1924 | 0.0000 | ||||||||||
| Volume | 3.00 | 0.0956 | 31.3715 | 0.0000 | ||||||||||
7. What is the equation of the cost function?
a. Cost = 14427
b. Cost =3.00 + 14427x
c. Cost = 25.1924 + 31.3715x
d. Cost = 14427 + 3.00x
8. What is the fixed cost?
a. 3.00
b. 1232.83
c. 14427
d. 31.3715
9. What is the variable cost?
a. 3.00
b. 1232.83
c. 14427
d. 31.3715
10. If each unit of this product sells for $10.00, how many units would need to be sold for the company to break even (cover the fixed and variable costs)?
a. 1110
b. 1443
c. 2061
d. 4809
11. Simplify 
a. x ≥ 3
b. x ≤ 3
c. x ≥ -3
d. x ≤ -3
12. Simplify 
a. 8xy
b. 4xy
c. 4x3y + 2x5y3
d. 6
13. One way to express revenue is by the number of units sold times the selling price for each unit. In this example, the number of units sold depends on price (p) and can be written as 
Write the function that expresses revenue as a function of price and simplify.
a. 
b. 
c. 
d. 
14. Profit is usually expressed as total revenue minus total cost. In this example, the selling price is $60 per unit, the fixed cost is $4500, and the variable cost is $18 per unit. Let x be the number of units made and sold and write the function that expresses profit as a function of x. Simplify the function as much as possible.
a. 42x + 4500
b. 42x - 4500
c. 78x - 4500
d. 78x + 4500
15. Combine this expression into one fraction.
a. 1
b. 21/45
c. 35/27
d. 8/45
