SUBJECT: MATH : Quantitative Methods for Business and Finance. Course Symbol: MAT 128

Please answer the questions below.

PLEASE DO NO WORRY ABOUT THE MARKS IN THE PARATHENSIS: EXAMPLE : 2 MARKS, 3 MARKS OR 4 MARKS. BECAUSE THEY ARE NOT PART OF THE QUESTIONS

D Question 1 2 pts 1. Assume the cost of making 40 coats is $900, the cost of making 44 coats is $940, and the cost equation is linear. The coats are sold for $31 each. (a) (2 marks) Find the marginal cost of production. (b) (3 marks) Find a linear equation in slope-intercept form that will represent the total cost of making x coats. (c) (2 marks) What is the fixed cost? (d) (2 marks) Find a profit equation in slope-intercept form that will represent the profit if x coats are made and sold. (e) (2 marks) Find the break-even point. addD Question 2 2 pts 2. Assume the book value, V, of a boat when it was new on January 1, 2020 is $34,000 and its book value decreases by $2,000 per year. The expected useful life of the boat is 14 years. (a) (2 marks) Assuming straight-line depreciation, find a linear function that gives the book value of the boat t years after its purchase as a new boat on January 1, 2020. (b) (3 marks) Sketch the graph of this linear equation. (c) (2 marks) Find the salvage value of the boat (defined to be its value after its expected life). (d) (3 marks) Find when the book value of the boat will be $27,000.D Question 3 8 pts 3. Assume that the following data is known for the cost, C, when x tables are made: Number of 40 45 50 55 tables, X: Cost, C: $600 $650 $710 $761 (a) (4 marks) Find the line of best fit (i.e., the least squares regression line) for all four of these data points. Use the line you found in part (a) to estimate (b) (2 marks) the cost if 49 tables are made; (c) (2 marks) the number of tables that can be made if $900 is available.D Question 4 3 pts 4. A survey of 900 people shows that 80 wear a mask, 169 wear glasses and 180 wear at least one of these two items. (a) (3 marks) Find how many people wear both a mask and glasses. (b) (3 marks) Draw and label a Venn diagram that numerically represents this data. (c) (3 marks) Estimate the probability that a person wears glasses, given that the person wears a mask