







A linear programming problem 
20130227 

From Kelley: A manufacturer of skis produces two types: downhill and crosscountry. Use the following table to determine how many of each kind of ski should be produced to achieve a maximum profit. What is the maximum profit? What would the maximum profit be if the time available for manufacturing is increased to 48 hours.

Downhill 
Crosscountry 
time available 
manufacturing time per ski 
2 hrs 
1 hr 
40 hr 
finishing time per ski 
1 hr 
1 hr 
32 hr 
profit per ski 
$70 
$50 

Answered by Penny Nom. 





Linear programming using the Simplex Method 
20091228 

From William: A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running,
at least three tons of ore must be processed each day. Ore from source A costs $20 per ton to
process, and ore from source B costs $10 per ton to process. Costs must be kept to less than $80 per day.
Moreover, Federal Regulations require that the amount of ore from source B cannot exceed twice the
amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B
yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to
maximize the amount of gold extracted subject to the above constraints?
I need a linear programming solution or algorithm of the simplex method solution.
Not a graphical solution. Thanks. Answered by Janice Cotcher. 





Linear programming 
20070424 

From Sylvia: What is graphing linear programming? Answered by Penny Nom. 





Linear programming 
20020527 

From Jes: A machine shop makes two parts, I and II, each requiring the use of three machines, A, B, C. Each Part I requires 4 minutes on Machine A, four minutes on Machine B and five minutes on machine C. Each Part II requires five minutes on Machine A, one minutes on Machine B and six minutes on Machine C. The shop makes a profit of $8 on each Part I and $5 on each Part II. However, the number of units of Part II produced must not be less than half the number of Part I. Also each day the shop has only 120 minutes of machine A, 72 minutes of Machine B, and 180 minutes of Machine C available for the production of the two parts. What should be the daily production of each part to maximize the shop's profit? Answered by Claude Tardif. 





Vitamins A and B 
20010114 

From Sara: A diet is to include at least 140 mg of Vitamin A and at least 145 mg of vitamin B. these requirements are to be obtained from two types of food. type X contains 10 mg of vitamin A and 20 mg of vitamin B per pound. Type Y contains 30 mg of vitamin A and 15 mg of vitamin B per pound. if type X food costs $12 and Type Y $8 per pound, how many pounds of each type of food should be purchased to satisfy the requirements at the minimum cost? Answered by Claude Tardif and Harley Weston. 





Pillows and Cushions 
20000927 

From Fiona:
The following problem was given to grade eleven algebra students as a homework assignment. To manufacture cushions and pillows, a firm uses two machines A and B. The time required on each machine is shown. Machine A is available for one full shift of 9.6 hours. Machine B is available for parts of two shifts for a total of 10.5 hours each day. Answered by Harley Weston. 





Linear programming and optimization 
19990409 

From Shams: What is Linear programming and optimization? Answered by Jack LeSage and Penny Nom. 





Operations Research 
19981008 

From Lisa Barrett: What is the history of operations research and the study of linear programming? Answered by Judi McDonald. 

