# ASSIGNMENT 5 Pizza Palace is running a promotional

## ASSIGNMENT 5 Pizza Palace is running a promotional

ASSIGNMENT 5 Pizza Palace is running a promotional

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Question 1 is based on the following information:
Pizza Palace is running a promotional sale on 2 litre bottles of Cola. The hope is to attract more customers into the shop who will also buy a pizza with two toppings at the regular price. They will lose R9,00 on every Cola order. The profit, however on each pizza will be R15,00. Let c represent the number of bottles of Cola sold and p the number of pizzas. Breaking even is the worst they are willing to accept. If they break even, the losses from the Cola sales will be equal to the profit from the pizza sales:

9c = 15p.

They want the losses from the Cola sales to be less than or equal to the profit from the pizza sales.

Question 1
Write an inequality for this situation. Graph the inequality by plotting the number of bottles of Cola sold on the horizontal axis and the number of pizzas sold on the vertical axis. Indicate the region where the Pizza Palace will profit from the promotion.

Question 3
Suppose you need to use at least R45,00 worth of stamps to mail a package. You have as many R3 stamps as you need, but only four R5 stamps. You want to determine how many of each stamp you have to use. Let x represent the number of R5 stamps you have to use. Let y represent the number of R3 stamps you have to use. Write a system of linear inequalities describing the possible number of each stamp you have to use. Determine one possible solution to the problem.

Question 4
A manufacturing company produces and sells bags. The cost (in rand) to manufacture y bags is given by the function

C(y) = 4y + 120√y + 4 000.

The approximate cost of manufacturing the 24th bag is calculated by determining the value of?

Question 5
The derivative of the function

f(x) = −3/4x2 + Ax3 +B/x

Question 6
If the derivative of a function is

f(x) =...