Please 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
The first one is correct, except I would have used "p" as the variable for "profit."
p = 3x + 5y
The second one is also correct. Again, I would have used "c" as the variable for "cost." It's just helpful to understand the relationship between the variables. I had a teacher who really hammered this concept.
c = .25x + .02y
(With or without the leading zeroes is fine.)
Your answers are correct.
For the first problem, since the profit per part A is $3.00 and the profit per part B is $5.00, the objective function that describes the total weekly profit would be z=3x+5y.
For the second problem, since the cost per ounce of chicken is $0.25 and the cost per ounce of potatoes is $0.02, the objective function that describes the total cost per patient per meal would be z=0.25x+0.02y.
Your answers to both problems are correct!
For the first problem, the objective function that describes the total weekly profit is indeed z = 3x + 5y. This equation calculates the profit by multiplying the number of part A produced (x) by its profit margin of $3.00 per part, and multiplying the number of part B produced (y) by its profit margin of $5.00 per part. Adding these two values together gives the total weekly profit.
Similarly, for the second problem, the objective function that describes the total cost per patient per meal is indeed z = 0.25x + 0.02y. This equation calculates the cost by multiplying the number of ounces of chicken purchased (x) by its cost of $0.25 per ounce, and multiplying the number of ounces of potatoes purchased (y) by its cost of $0.02 per ounce. Adding these two values together gives the total cost per patient per meal.
Well done!