The multivariate demand function below will be needed for questions 12-18.

Setting: Grapple, Inc. is a leading seller of laptop personal computers.However, they want to become a leading tablet seller, too.Your marketing department, aided by your economics staff, has estimated a function to help you in the quest for market leader in tablets.The variables are defined after the function.

Q_g= 10000 - 25P_g+ 20P_h+ 30P_r- 15_dv- 35P_sc- 10P_mm+ 0.05A_g+ 0.03A -25C + 0.1Y

Q_g = the number of Grapple tablet computers demanded per week.

P_g = the price of each new Grapple tablet (in $).

P_h = the price of each Hewpaq tablet (in $).

P_r = the price of each Ronova tablet.

P_dv = the price to equip a tablet with Holographic digital video (in $, this is an upgrade option that enables three-dimensional graphics on a tablet.Two-dimensional graphics is standard equipment).

P_sc = the price of various screen sizes (in $, a 8 inch is standard, but upgrade options are 10 inch extra sharp, 12 inch, 12 inch extra sharp, Each also has a touch-screen option.The upgrades get progressively more expensive as the size and capability increases).

P_mm = the price of memory chip upgrades (in $).More 2 Gigabyte (Gb) chips can be added. Of course each added 2 Gb chip costs more.One 2 Gb chip is standard.

Y = average annual disposable income of a typical tablet purchaser (in $).

A_g = average age of a tablet purchaser (in years).

A = average annual Grapple advertising expenditure (in $).

C = number of computer systems the average tablet purchaser already owns.

12.If all variables remain unchanged except the price of Hewpaq (P_h) laptops, which increases by $50, then the demand for Grapple tablets will:

12a. decrease by 1000

b. decrease by 1250

c. increase by 1000

d. increase by 1250

13.If all variables remain unchanged except the price of Holographic digital video (P_dv), which increases by $50, then the demand for Grapple tablets will:

13 a. decrease by 750

b. decrease by 1500

c. decrease by 1750

d. increase by 750

e. increase by 1500

f. increase by 1750

14.If all variables remain unchanged except the price of memory chips (P_mm), which increases by $20 per chip, then the demand for Grapple tablets will:

14a. increases by 200

b. decreases by 200

c. increases by 450

d. decreases by 450

15.You can tell by the sign preceding the Income variable (Y) that Grapple tablets are:

15a. normal goods

b. substitute goods

c. inferior goods

d. complementary goods

In the questions 16-18 use these values in the multivariate demand function for Grapple tablets:

P_g = $500P_h= $600P_r = $600P_dv = $50P_sc = $100P_mm = $30A_g = 40

A = $100,000C = 2Y=$30,000

16.After the values above are entered into your demand function, what quantity of Grapple tablets will be demanded?Be very careful with this calculation.This value will be used again below.

16.a19401b 28902c 31027d 35902e 38902f 40152

17.What is the point cross-price elasticity of Grapple tablets at the above price of Hewpaq laptops (P_h)? Show the values you use in the formula and work out completely.Be sure to show the sign.Does this value indicate a very sensitive (elastic; responsive) relationship ( comment)?The formula is:

E =Q_g/P_h* P_h/Q_g

17. Work elasticity out in detail, give your calculations below.Next, comment addressing the question asked.

18. What is the point age elasticity of Grapple tablets at the above age level (A_g)?Show the values you use in the formula and work out completely.Be sure to show the sign.Does this value indicate a very sensitive (elastic; responsive) relationship ( comment)?The formula is:

E =Q_g/A_g* A_g/Q_g

18.Work elasticity out in detail, give your calculations below.Next, comment the question asked.

19.Write the first derivative of the following function

V = 60 - S + 3S³- 2S⁴

20.Write the first derivative of the following function

U = 10T - 2T^-3+ 3T⁴- 4T^1/4