Afeasible region is bounded by the constraints: 20 20 4 5 0.25 y x y x y x            the objective function is p = 3x + 5y. (a) graph the feasible region.

(b) find the value of the objective function at each vertex of the feasible region 

(c) what is the minimum  value of the objective function, p?

(d) at which vertex point does the minimum value occur?

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2. in 2010, the population of a town was 8500. the population decreased by 4.5% each year.

(a) write an equation to find the population of the town t years after 2010.

(b) in what year will the population of the town be 7000? show your work.

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In the triangles, bc =de and ac fe.if the mzc is greater than the mze, then ab isdfelth

3women sell hats at a craft fair weekly. the money they make at the fair is split into categories. 9% goes to pay taxes. $55 goes to pay rent for the space they sell in. the rest is split between the women. if the group make $706 at the fair, how much does each women get paid once the money is divided

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?