Wivco produces two products: 1 and 2. The relevant data are shown in Table. Product 1 Product 2
Selling price $15 $8
Labor required 0.75 hour 0.50 hour
Machine time required 1.5 hours 0.80 hour
Raw material required 2 units 1 unit
Each week, as many as 400 units of raw material can be purchased at a cost of $1.50 per unit. The company employs four workers, who work 40 hours per week(their salaries are considered a fixed cost). Workers can be asked to work overtime and are paid $6 per hour for overtime work. Each week, 320 hours of machine time are available.
In the absence of advertising, 50 units of product 1 and 60units of product 2 will be demanded each week. Advertising can be used to stimulate demand for each product. Each dollar spent on advertising product 1 increases its demand by 10units; each dollar spent for product 2 increases its demand by15 units. At most $100 can be spent on advertising. Define
P1 = number of units of product 1 produced each week
P2 = number of units of product 2 produced each week
OT = number of hours of overtime labor used each week
RM = number of units of raw material purchased each week
A1 = dollars spent each week on advertising product 1
A2 = dollars spent each week on advertising product 2
Then Wivco should solve the following LP:
width=
All variables non-negative
Use LINDO to solve this LP. Then use the computer output to answer the following questions:
a If overtime were only $4 per hour, would Wivco use it?
b If each unit of product 1 sold for $15.50, would the current basis remain optimal? What would be the newoptimal solution?
c What is the most that Wivco should be willing to pay for another unit of raw material?
d How much would Wivco be willing to pay for another hour of machine time?
e If each worker were required (as part of the regular work week) to work 45 hours per week, what would the company’s profits be?
f Explain why the shadow price of row (1) is 0.10.
g Wivco is considering producing a new product (product3). Each unit sells for $17 and requires 2 hours of labor, 1 unit of raw material, and 2 hours of machine time. Should Wivco produce any of product 3?
h If each unit of product 2 sold for $10, would the current basis remain optimal?