kane manufacturing has a division that produces two models of fireplace grates, x units of model a and y units of model b. to produce each model a grate requires 3 lb of cast iron and 6 min of labor. to produce each model b grate requires 4 lb of cast iron and 3 min of labor. the profit for each model a grate is $1.50, and the profit for each model b grate is $3.50. also, 1000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day.
because of a backlog of orders for model a grates, kane's manager had decided to produce at least 150 of these grates a day. operating under this additional constraint, how many grates of each model should kane produce to maximize profit?
(x, y) = 150,100
what is the optimal profit?
$

a box 3 3/4 feet long or 4+ feet.

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

hey! so 1 (25) out of 4 (100) is 25 so your answer is 25%. it's like quarters!