1. Shoe Manufacture
A small shoe manufacturer makes two styles of trainers, a cross-training shoe and a
specialist running shoe. A pair of cross-training shoes requires 1 hour machining
and 2 hours assembly and makes a profit of £10. A pair of running shoes requires
1.5 hours machining and 1.5 hours assembly, and makes a profit of £15. The
company has 210 hours machining time available per week and 300 hours assembly
time per week.

Let x denote the number of pairs of cross-trainers and y denote the number of pairs
of running shoes the manufacturer can produce per week.

(a) What is the weekly profit of the manufacturer, assuming that the demand for
trainers means that all pairs will be sold?

(b) Write down all the constraints for the problem.

(c) Solve the linear programming problem graphically to find the number of trainers
of each type that maximise the revenue. On your graph indicate clearly the
feasible region, the optimal point, an arbitrary isoprofit line, and the isoprofit line
corresponding to optimal profit.

(d) Hence state the optimum number of trainers of each type the manufacturer
should produce each week, and the maximum profit the manufacturer can
make.

Solution Summary

An LP problem is solved using a graphical method. The solution is detailed and well presented.

WORLEY FLUID SUPPLIES PRODUCES THREE TYPES OF FLUID HANDLING EQUIPMENT CONTROL VALVES, METERING PUMPS AND HYDRAULIC CYLINDERS/ ALL THREE PRODUCTS REQUIRE ASSEMBLY AND TESTING BEFORE THEY CAN BE SHIPPED TO CUSTOMERS
CONTROL VALVE METERING PUMP HYDRAULIC CYLIND

A linear program has the objective of maximizing profit = 12X + 8Y. The maximumprofit is $8,000. Using a computer we find the upper bound for profit on X is 20 and the lower bound is 9. Discuss the changes to the optimal solution (the values of the variables and the profit) that would occur if the profit on X were increased to

Linearprogramming
Items X1 X2
Profit per Item 3 6
Resource constraints Available Usage Left over
1 7 3 40 0 40
Output
X1= 0
X2= 0
Z= 0
Solve the following linearprogramming model by using the computer
Minimi

PLEASE EXPLAIN YOUR ANSWERS (why did you choose T instead of F or A instead of C, etc.).
C 1. Which of the following is not a component of the structure of a linearprogramming model?
a. parameters
b. decision variables
c. environment of certainty
d. constraints
F 2. In a linearprogramming model, the numb

See attached file.
The board of directors of General Wheels Co. is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following ta

Question: Cully furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 c

A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows.
Hours/Unit
Product Line 1 Line 2
A 12 4
B 4

Problem 3: LinearProgramming
I have a six acre farm that I can use for the productionof rice (X1) or corn (X2). I have also
27 days of labor and 32 tons of fertilizer.
One acre of rice requires three days of labor and eight tons of fertilizer, while one acre of corn
requires ni