A company supplies 75-centiliter glass bottles to beverage manufacturers all around Europe. The company's best selling products are wine bottles and...

A company supplies 75-centiliter glass bottles to beverage manufacturers all around Europe. The company's best selling products are wine bottles and champagne bottles. Wine bottles are sold at a price of 3euro/unit, and champagne bottles are sold at 3.5 euro/unit.

These two products can be manufactured in three different production lines: PL1, PL2 and PL3. These production lines present a different variable cost per unit per product (see Table 1). They also have a limited capacity of 1000 bottles for PL1, 1500 bottles for PL2 and 2800 bottles for PL3.

Table 1: Variable production cost per unit (in euros/unit)

wine bottle

champ bottle

PL1

0.77

0.95

PL2

0.59

0.59

PL3

0.62

0.79

There is also a limited availability of two important raw materials: 1000kg of silica sand (the major component in each bottle), and 300 kg of iron oxide (the component that gives the bottle a green color). Wine bottles and champagne bottles use different amounts of these raw materials (see Table 2).

Table 2: Raw material need per unit produced (in kg/unit)

wine bottle

champ bottle

silica

0.2

0.25

iron

0.08

0.06

Assuming that demand is unlimited (all bottles produced are sold), solve a model to decide which production plan would maximize profit.

What is the maximum profit Comapany could make under the conditions specified in this problem?

Round your answer to the nearest integer.

Question 2

Comapany is going to launch a new product: soda bottles. The estimated demand for this new product is 5000 units. The objective of the company is to produce these new type of bottles at the lowest cost. Soda bottles have a smaller size than 75-centiliter bottles and use specific additives. Therefore, although they can be produced in some of the existing production lines of the company, there is a set up cost associated with preparing the line to manufacture soda bottles. The company has three production lines (PL4, PL5 and PL6) with some spare capacity that could be used to manufacture soda bottles. But the operations manager has made very clear that there is a minimum production requirement, to make it worth the effort of adjusting the parameters of each machine. All the detailed information per production line can be found in Table 3.

Table 3: Costs (in euros) and min/max production requirements (in units) per production line.

cost per unit

set up cost

min production

max production

PL4

0.46

500

1000

3000

PL5

0.66

700

500

4000

PL6

0.5

400

900

2500

solve a model that helps you decide how much to produce in each line to minimize total production cost of soda bottles. (Note: Demand must be met, therefore you must plan on producing at least 5,000 units/month.)

What is the minimum production cost of soda bottles under the conditions specified in Question 2?

Round your answer to the nearest integer.

Question 3

The marketing department of company has been doing some market analysis and they came to the conclusion that the demand for the new soda bottles is highly dependent on the price point. If the price is too low, customers will believe the product is of low quality, and if the price is too high, customers will look for other suppliers. They have created the following equation that relates demand with price:

Demand=−387p2+1000p+5000

According to the marketing department, what would be the optimal price to maximize demand?

Round your answer to three decimal places.