3. Linear Programming: An athlete carefully watches her intake of calcium, proteins, and calories. Her breakfast diet consist mainly of milk and cereal whose prices and nutrient contents appear in the following table:

Milk (X1) Cereal(X2)

Calcium 2 2

Protein 2 6

Calories 6 2

Cost (/unit) $0.10 $0.15

She seeks a diet that supplies at least 50 units of calcium, 90 units of protein, and 66 units of calories at minimum cost

a. Formulate the object and constraint functions

b. Find the cost minimizing units of milk and cereal.

c. What is the minimum cost of meeting the nutrient requirements?

4. The manager of a supermarket lowers the price of its 24-pack bottled water from 4.60 to 3.40 and as a result sales of bottled water increases from 400 to 600 packs

a. What is the arc price elasticity of demand for bottled water?

b. Give an economic interpretation to the numerical value obtained in part a.

c. Based on your answer to (a), would it have been appropriate to mark down price in order to increase total revenue? Why?

d. What are some of the applications (uses) of the concept of price elasticity of demand?

5. The research department of the Corn Flakes Corporation (CFC) estimated the following regression for the demand of the cornflakes it sells:

QX = 1.0 – 2.0PX + 1.5I + 0.8PY – 3.0Pm + 1.0A

Qx = sales of the CFC cornflakes, in millions of 10-ounce box

PX = the price of CFC cornflakes, in dollars per 10-ounce box

I = personal disposable income in thousands of dollars

PY = the price of competitive brand of cornflakes, in dollars per 10 ounce box

Pm = price of milk in dollars per quart

A = advertising expenditures of CFC cornflakes, in hundreds of thousands of

dollars per year

This year PX = $2, I = $4, PY = $2.50, Pm = $1, and A = $2

a. Find sales of CFC cornflakes this year.

b. Calculate the elasticity of sales with respect to each variable in the demand function

c. Based on your answer to (b), what should CFC’s pricing policy be if ut wants to increase sales revenue? Justify.

d. Estimate the level of sales next year if CFC reduces PX by 10 percent, increases advertising by 20 percent, I rises by 5 percent, PY is reduced by 10 percent, and Pm remains unchanged.

Milk (X1) Cereal(X2)

Calcium 2 2

Protein 2 6

Calories 6 2

Cost (/unit) $0.10 $0.15

She seeks a diet that supplies at least 50 units of calcium, 90 units of protein, and 66 units of calories at minimum cost

a. Formulate the object and constraint functions

b. Find the cost minimizing units of milk and cereal.

c. What is the minimum cost of meeting the nutrient requirements?

4. The manager of a supermarket lowers the price of its 24-pack bottled water from 4.60 to 3.40 and as a result sales of bottled water increases from 400 to 600 packs

a. What is the arc price elasticity of demand for bottled water?

b. Give an economic interpretation to the numerical value obtained in part a.

c. Based on your answer to (a), would it have been appropriate to mark down price in order to increase total revenue? Why?

d. What are some of the applications (uses) of the concept of price elasticity of demand?

5. The research department of the Corn Flakes Corporation (CFC) estimated the following regression for the demand of the cornflakes it sells:

QX = 1.0 – 2.0PX + 1.5I + 0.8PY – 3.0Pm + 1.0A

Qx = sales of the CFC cornflakes, in millions of 10-ounce box

PX = the price of CFC cornflakes, in dollars per 10-ounce box

I = personal disposable income in thousands of dollars

PY = the price of competitive brand of cornflakes, in dollars per 10 ounce box

Pm = price of milk in dollars per quart

A = advertising expenditures of CFC cornflakes, in hundreds of thousands of

dollars per year

This year PX = $2, I = $4, PY = $2.50, Pm = $1, and A = $2

a. Find sales of CFC cornflakes this year.

b. Calculate the elasticity of sales with respect to each variable in the demand function

c. Based on your answer to (b), what should CFC’s pricing policy be if ut wants to increase sales revenue? Justify.

d. Estimate the level of sales next year if CFC reduces PX by 10 percent, increases advertising by 20 percent, I rises by 5 percent, PY is reduced by 10 percent, and Pm remains unchanged.

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