Mathematics for Business Decisions, Part IIHomework 2Mathematics for Business Decisions, Part IIHomework 2forMath 115b, Section: Instructor: James BarrettDate: byTeam: We, the undersigned, maintain that each of us participated fully and equally in the completion of this assignment and that the work contained herein is original. Furthermore, we acknowledge that sanctions will be imposed jointly if any part of this work is found to violate the Student Code of Conduct, the Code of Academic Integrity, orthe policies and procedures established for this course. Name Typed Signature % of Grade__________________ ______________________________ ______________________________ ______________________________ ______________________________ ______________________________ ______________________________ _____________________________ _______________________________ _____________________________ ____________1. Experiment with different values in Cell B19 of the sheet Income in Dinners.xlsm. (i) Find the number of dinners that would be sold at a price of $19.95. (ii) What revenue can be expected if dinners are priced at $19.95Print out the computation chart.?Solution:2. Suppose that the demand function for a good is given by D(q )=−0 .1⋅q+150. (i) Use Graphing.xls to plot D(q ) and the revenue function, R(q ). (ii) Estimate the price that will yield the greatest revenue. Print out the computation chart.Solution:3. The demand function for a new type of car alarm system is shown in the following plot. DEMAND FUNCTION01002003004005000 100 200 300 400 500 600q in K'sD (q ) in $Note that the quantities sold are given in thousands. Estimate the revenue (in dollars) from selling 300,000 alarms.Solution:4. (i) Use your team’s data and Trend Lines to find the formula for a quadratic demand function. (ii) Plot D(q ) and R(q )for your team’s product. Use the same units as in the work on the class project in the sheet Functions of Marketing Focus.xls.Show a table of National Market Sales and Price.Solution:5. (i) Experiment with computation in the sheet Profit of Dinners.xls to find the number of dinners that could be sold at a price of $18. (ii) Find the cost of preparing these dinners. (iii) What profit can be expected from preparing and selling buffalo steak dinners at $18?Solution:6. Estimate the percentage drop in weekly profit that would result from dropping the price of buffalo steak dinners from $22 to $20.Solution:7. Use the graphs in this section of the text to estimate the weekly profit that would resultfrom spending $30,000 to prepare buffalo steak dinners.Solution:8. Refer to the demand function given in Exercise 3 in the text . Suppose that the fixed cost for producing this good is C0=$ 12 , 000 and that the variable costs are given byVC(q)=1300⋅√q. (i) Use Graphing.xls to plot C(q) and P(q ). (ii) Use your graphs to estimate the number of units that should be produced, and how they should be priced in order to attain the maximum profit. (iii) Approximately what maximum profit might be expected?Solution:9. Refer to the demand function whose graph is shown in Exercise 5 in the text. The plotof the cost function for the alarms is given below. COST FUNCTION0204060801001201400 100 200 300 400 500 600q in K'sC (q ) in millions of $Note that the quantities of alarms are given in thousands and the total costs are given in millions of dollars. (i) Estimate the number of alarms that would be sold at a price of $250 each. (ii) Estimate the revenue (in dollars) that would result from the sale of alarms priced at $250. (iii) Estimate the cost (in dollars) of producing the alarms that would be sold at $250. (iv) Estimate the profit (in dollars) that would result from the saleof alarms at $250.Solution:10. (i) Use your team’s data to find the formula for the cost function of your product. (ii)Plot C( q)and P(q ) for your team’s data. (iii) Plot C(q) and r(q) on the same axis. Use the same units as in the work on the class project in the sheet Functions of Marketing Focus.xls. Answer the first three questions for your project. How many units at what price will produce the maximum profit? What is the maximum
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