40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Design & Measurement Lesson: DM-L4 Budget Constraints Budget Constraints Learning Outcome B-4 DM-L4 Objectives: To plan and cost projects with pre-determined budgetary constraints.

40S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Design & Measurement Lesson: DM-L4 Budget Constraints When designing a construction project, you usually need to pay close attention to the costs. You will probably have a budget that you should not exceed. The costs include the construction materials, labour, taxes, insurance, permits, and so on. The design of the project may have to be altered if the costs exceed the budget. Theory – Intro

40S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Design & Measurement Lesson: DM-L4 Budget Constraints You plan to build a patio with paving stones in the backyard. A diagram of the backyard is shown below. Sample Problem

40S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Design & Measurement Lesson: DM-L4 Budget Constraints The budget for this project is $ Design the largest functional patio that remains within this budget. State the shape and dimensions of the patio that you design, and state why you chose this design. Also provide a cost analysis of the patio. Identify and explain any assumptions that you make. Sample Problem – cont’d

40S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Design & Measurement Lesson: DM-L4 Budget Constraints Budget: $ Sample Problem – cont’d The costs are as follows: paving stones$50.00/m 2 sand$25.00/m 3 incidental costs$75.00 Other factors to consider are: paving stones must be laid on a bed of sand 10-cm thick you need to buy 10 percent more paving stones to make up for breakage and cutting waste all costs are subject to 7 percent PST and 6 percent GST

40S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Design & Measurement Lesson: DM-L4 Budget Constraints In order to find the largest possible size of the patio, you need to find the cost per square metre for the patio. Once you have this figure you can divide it into the available money to find the total possible area for the patio. The only task left then will be to draw into the diagram any functional patio that fits the area. Functional issues could be: access to the back door; not too narrow or too wide; not on the back lane; et cetera. Sample Problem – cont’d

40S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Design & Measurement Lesson: DM-L4 Budget Constraints Cost-per- m 2 calculation: Sand costs: $25.50/m 3 = $2.55/m 2 at 10cm thick. Stones cost $50.00 x 1.10 = $55.00/m 2 with the waste included. Total cost per m 2 = ($ $2.55)*1.14 = $57.55 x 1.14 = $65.61 with taxes. Available money starts at $ Subtract the incidentals with taxes included. $75.00 x 1.14 = $ Available: $ $85.50 = $ Total area of your patio could then be: $914.50/$65.61 = m 2. This would indicate that the area of your patio cannot be larger than m 2. The shape is your own design. The design shown on the next slide is a square with side length Note that it has access to the back door and fits in the backyard. The patio is indicated in by the khaki colour. Sample Problem – Solution

40S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Design & Measurement Lesson: DM-L4 Budget Constraints Sample Problem – Solution cont’d