the manager of a senior housing unit wants to provide nutritious meals at minimal cost. Adults need at least 400 units of protein and at least 180 unit(cont) of iron. Steak costs \$.10 per ounce...

the manager of a senior housing unit wants to provide nutritious meals at minimal cost. Adults need at least 400 units of protein and at least 180 unit

(cont) of iron. Steak costs \$.10 per ounce and eachounce provides 40 units of protein and 15 of iron. Liver costs \$.30 per ounce and each ounce provides 15 units of protein and 30 of iron. Adults want a portion of steak to weigh atleast 6 ounces, and expect to have at least a 4 ounce portion of liver. Please set up, and solve this problem as a linear program. Define the variables in the equations, and write out the objective function and each one of the constraints.

rcmath | Certified Educator

Let x the number of oz of steak needed, and y the number of oz of liver needed.

The objective function will be `.10x+.30y`

The constraint `x>=6`

` `

`y>=4`

The equations

`40x+15y>=400`

`15x+30y>=180`

To solve this system we need to multiply the first inequality by 2, then subtract the second inequality from it.

`80x+30y>=800`

`15x+30y>=180`

` ` `65x>=620`

`x>=124/13~~9.5`

Substitue x in either of the equations we get `y>=1.3`

The second constraint make it mandatory for `y>=4`

Note: To minize cost, since we are obligated to use at least 4 oz of the more expensive product, if I plug the 4 back in the first equation, we find that it give us `x>=8.5`

So buying at least 8.5 oz of steak and 4 oz of liver will be sufficient.

rcmath | Certified Educator

Another note: We ususally solve system of inequality graphically and not the way I did it. What I did was really solve for =,and then use the constraint to figure out the final answer.