Question

The manager of a take-out pizza store needs to hire pizza makers and cashiers for the evening shift. The total number of employees of both kinds can be at most 16 and the ratio of cashiers to pizza makers must be at least 3 to 5. Also, each pizza maker can answer 12 phone calls per hour and each cashier can answer 4 calls per hour while the pizza shop must be able to handle at least 72 calls during peak hours.
(a) Create and graph a system of linear inequalities to model this problem
(b) Identify the solution region
(c) If each pizza maker gets $10 per hour and each cashier gets $6 hour, how many
pizza makers and how many cashiers should the manager hire in order to minimize
her cost?

Answer 1

Answer:

a) x + y ≤ 16

y/x ≥ 3/5

12*x + 4*y ≥ 72

b) see picture attached

c) 5 pizza makers and 3 cashiers should be hired.

Step-by-step explanation:

a) Let's define:

x: amount of pizza maker

y: amount of cashier

From conditions in the question:

x + y ≤ 16

y/x ≥ 3/5

12*x + 4*y ≥ 72

b) In the picture attached, the feasible region (also called solution region) is shown.

c) We want to minimize:

10*x + 6*y

subject to the previous restrictions.

It is known that the optimum solution is on the vertex of the feasible region (it is a linear system). Evaluating cost function at each point, we get:

10*1 + 6*15 = 100

10*5 + 6*3 = 68

10*10 + 6*6 = 136

Then, 5 pizza makers and 3 cashiers should be hired.