1. ## Linear Programming-Check my answers

Solve the problem.

A steel company produces two types of machine dies, part A and part B. The company makes a $3.00 profit on each part A that it produces and a$5.00 profit on each part B that it produces. Let x= the number of part A produced in a week and y= the number of part B produced in a week. Write the objective function that describes the total weekly profit.

I got: z=3x+5y

A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $0.25 and an ounce of potatoes for$0.02 Let x= the number of ounces of chicken and y= the number of ounces of potatoes purchased per patient. Write the objective function that describes the total cost per patient per meal.

I got: z=0.25x+0.02y

A steel company produces two types of machine dies, part A and part B and is bound by the following constraints:
∙ Part A requires 1 hour of casting time and 10 hours of firing time.
∙ Part B requires 4 hours of casting time and 3 hours of firing time.
∙ The maximum number of hours per week available for casting and firing are 100 and 70, respectively.
∙ The cost to the company is $0.75 per part A and$3.00 per part B. Total weekly costs cannot exceed $45.00. Let x = the number of part A produced in a week and y= the number of part B produced in a week. Write a system of three inequalities that describes these constraints. I got: x+10y< or equal to 100 4x+3y< or equal to 70 0.75x+3y< or equal to 45 A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for$0.25 and an ounce of potatoes for $0.02. The dietician is bound by the following constraints. ∙ Each ounce of chicken contains 13 grams of protein and 24 grams of carbohydrates. ∙ Each ounce of potatoes contains 5 grams of protein and 35 grams of carbohydrates. ∙ The minimum daily requirements for the patients under the dietitian's care are 45 grams of protein and 58 grams of carbohydrates. Let x = the number of ounces of chicken and y= the number of ounces of potatoes purchased per patient. Write a system of inequalities that describes these constraints. I got: 13x+24x> or equal to 45 5y+35y > or equal to 58 Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 5 hours to make a hat and 3 hours to make an afghan, and she has no more than 41 hours available. She has material for no more than 11 items, and she wants to make at least two afghans. Let x = the number of hats she makes and y = the number of afghans she makes. Write a system of inequalities that describes these constraints. I got: 5x+3y< or equal to 41 x+y< or equal to 11 y > or equal to 2 An office manager is buying used filing cabinets. Small file cabinets cost$5 each and large file cabinets cost $8 each, and the manager cannot spend more than$72 on file cabinets. A small cabinet takes up 7 square feet of floor space and a large cabinet takes up 10 square feet, and the office has no more than 96 square feet of floor space available for file cabinets. The manager must buy at least 7 file cabinets in order to get free delivery. Let x = the number of small file cabinets bought and y = the number of large file cabinets bought. Write a system of inequalities that describes these constraints.

I got:

5x+8y< or equal to 72
7x+10y < or equal to 96
y> or equal to 7

2. Hello, soly_sol!

You've switched some of your variables . . .

A company produces two items: part A and part B.
Part A requires 1 hour of casting time and 10 hours of firing time.
Part B requires 4 hours of casting time and 3 hours of firing time.
The maximum number of hours per week available for casting and firing are 100 and 70, resp.
The cost to the company is $0.75 per part A and$3.00 per part B.
Total weekly costs cannot exceed \$45.00.

Let x = the number of part A produced in a week
and y= the number of part B produced in a week.
Write a system of three inequalities that describes these constraints.
I suggest organizing the information . . .

$\begin{array}{cccccccc}& |& \text{casting} &|& \text{firing} &|& \text{cost} &| \\ \hline\text{part A }(x) &|& x &|& 10x &|& 0.75x &| \\\text{part B }(y) &|& 4y &|& 3y &|& 3.00y &| \\ \hline\text{total} &|& 100 &|& 70 &|& 45.00 &|\end{array}$ . . Then read down the columns

The system is: . $\begin{array}{ccc}x + 4y & \leq & 100 \\ 10x + 3y & \leq & 70 \\ 0.75x + 3.00y & \leq & 45.00 \end{array}$